Date: 5:40-6:40pm on Wednesday 4/20
Location: HOA 160
Speaker: Tess Anderson
Bio: Professor Tess Anderson is currently at Purdue University, where she studies the interplay of harmonic analysis and number theory. This fall, she will be joining us at CMU.
Title: Let's count things: Arithmetic statistics meets Fourier analysis
Abstract: Arithmetic statistics is an area devoted to counting a wide range of objects of algebraic interest, such as polynomials, fields, and elliptic curves. Fueled by the interplay of analysis and number theory, we'll count polynomials and number fields. How often does a random polynomial fail to have full Galois group? How many number fields of a given degree and bounded discriminant are there? In nontechnical terms: let's count things together!
Date: 5:40-6:40pm on Wednesday 4/13
Location: HOA 160
Speaker: Varun Gudibanda
Bio: Varun is a PhD student at UW Madison and is an alum of CMU's math department. His interests are in mathematical physics and PDEs. He also started the "Today I did x" email intro to math club emails!
Title: It's Getting Hot In Here Let's Study Heat Convection
Abstract: Have you ever boiled water? If so, you’re familiar with the concept of convection. But did you know that one single number involving convection has divided a research community? Come to this week's talk to find out about the world of convection and this one number that has been debated for decades.
Date: 5:40-6:40pm on Wednesday 3/23
Location: HOA 160
Speaker: Robert Pego
Bio: Dr. Pego is a professor here at CMU interested in analysis, dynamics, and PDEs. His work is often motivated by fluids, physics, and even population ecology!
Title: How to count fish using mathematics
Abstract: In 2003 the Japanese fisheries scientist H.-S. Niwa published a remarkable study of the distribution of sizes of schools of fish in the mid-ocean. Niwa's ideas led to studying an infinite set of kinetic equations for the merging and splitting of animal groups. We explain the non-Gaussian nature of the equilibrium school-size distribution using complex-function theory for Bernstein functions (related to Laplace transforms). For this we make use of a new double-transform theorem, which touches on a diverse collection of topics across mathematics: generating functions for Hausdorff moment sequences, Fuss-Catalan numbers, convolution semigroups, and a striking integral formula for binomial coefficients.
Date: Wednesday, March 16, 2022
Location: 5:40-6:40pm HOA 160
Speaker: Ian Tice
Bio: Prof. Tice is a professor here at CMU interested in analysis and PDES. He's also involved with the honors program here!
Abstract: Banach spaces are essential tools in infinite dimensional analysis because they serve as useful container spaces in which to construct various interesting mathematical objects (solutions to differential or functional equations, pathological functions, integrals, generalized limits, notions of fractional derivatives, etc). Due to their ubiquity in modern analysis, it is often convenient to have tools for constructing new Banach spaces that interpolate between a pair of given spaces. In this talk we will give a completely elementary but nontrivial example of how one might go about constructing such interpolation spaces. We will use nothing more than one dimensional calculus (continuity and the fundamental theorem of calculus) and basic linear algebra.
Date: TUESDAY, March 15, 2022
Location: 4:30 P.M., WeH 7218 & Zoom
Speaker: Terrance Pendleton, Drake University
Title: The Camassa-Holm Equation: Analysis, Numerics, Generalizations and Applications
Abstract: In this talk, we study the dynamics of the interaction among a special class of solutions of the one-dimensional Camassa-Holm equation and its generalizations. The equation yields soliton solutions whose identity is preserved through nonlinear interactions. These solutions are characterized by a discontinuity at the peak in the wave shape and are thus called peakon solutions. We apply a variety of numerical methods to study both the analytical and physical properties of the Camassa-Holm equation and show its potential for modeling the propagation of tsunami waves. In particular, we provide global existence and uniqueness results for the Camassa-Holm Equation by establishing convergence results for the particle method applied to these equations, and then use this same method to numerically quantify the nonlinear interaction among the peakon solutions. We conclude the talk by proposing new invariant-preserving finite difference schemes for a generalization of the Camassa-Holm equation as a potential model for the propagation of tsunami waves.
Date: 5:40-6:40pm on Wednesday, 3/2
Location: HOA 160
Speaker: Simran Khunger
Bio: Simran Khunger is the math club president. She's currently a senior preparing to go off to graduate school!
Title: So you want to go to grad school?
Abstract: Our math club president Simran Khunger will be giving a talk "So you want to go to grad school?". She'll explain the math grad admissions process, what opportunities CMU math students have for each of their undergrad years, and her experience going through the graduate process herself. There will also be a part at the end discussing post-grad school careers and applying to non-math grad programs. This is a great opportunity for underclassmen to hear about what grad school is like, how to get there, and whether or not it's right for you!
Date: Wednesday, 2/23, 5:40-6:40pm
Location: Porter Hall A18B
Speaker: Andrew Newman
Bio: Andrew is a postdoc at CMU who's interested in the intersection of probability, topology, and combinatorics. He might be your 21-325 professor!
Title: An introduction to stochastic topology!
Abstract: Over the last 50 years, mathematicians have been able to study random graphs to answer questions about what graphs typically look like. A graph though, is just 1-dimensional; it's built out of lines and points. In this talk we'll discuss what random higher-dimensional spaces are, why they are worth studying, and overview the basic ideas from topology that allows us to understand and, sometimes, answer questions like: What is the expected number of 10-dimensional holes in a random 11-dimensional object, or what is the probability that a random 12-dimensional shape can be drawn in 24-dimensional space? The only background knowledge that will be assumed is a basic familiarity with matrices.
Date: Tuesday, 2/15, 5:40-6:40pm
Location: Zoom
Speaker: Zoe Wellner
Bio: Zoe is a 4th year grad student in the math department's ACO program who has a very cute cat (see the flyer)! The title and abstract are also attached below!
Title: Adventures in Weird Geometries
Abstract: Looking at drawings, Pac-man’s universe, or even the ground we walk on, many things appear “flat”. Looking at space locally only tells us so much about the fundamental properties of the space itself. It can be extremely valuable to consider problems in spaces where they naturally reside. Mathematically, if we have a problem that loops in on itself we might want to consider solving that problem on a torus. If we need to differentiate the parity of an object, maybe it lives in a Möbius strip? If we are looking to accurately represent what we see around us in a drawing on a piece of paper, we are using the properties of projective space! We will discuss how these differ mathematically and the different objects these connect with.
Date: Wednesday, 2/2, 5:40-5:50pm
Location: Zoom
Speaker: Alec Sun
Bio: Alec is a grad student in the math department interested in combinatorics and theoretical CS. He is also a TA for Probability and Computing this semester!
Title: Sperner's Lemma
Abstract: Sperner's Lemma is a combinatorial analog of Brouwer's Fixed Point Theorem. Given a triangle ABC with triangulation T, suppose that the set of vertices of T is colored in 3 colors such that A, B, C are colored 1, 2, and 3, and the color of each vertex on an edge of ABC is the same as one of its endpoints. Sperner's Lemma states that there exists a triangle from T whose vertices are colored with 1, 2, and 3. After sketching a proof, we will see how Sperner's Lemma can be applied to resolve fair division problems as well as establish the Brouwer's Fixed Point Theorem.
Date: Thursday, 1/27/22, 5:40-6:40PM
Location: Zoom
Speaker: Misha Lavrov
Bio: Misha Lavrov is formerly a graduate student at CMU, and currently a math professor at Kennesaw State University in Georgia who occasionally writes about himself in the third person. His interests mathematical and nonmathematical include graph theory, baking cookies, probability, playing board games, and very large numbers
Title: The Mathematics of Sproutball
Abstract: Sproutball is a variant of dodgeball which is exceptionally good at entertaining small children for almost arbitrarily long periods of time. But for how long exactly? We will find out. Along the way, we'll take an excursion into the theory of excursions, a tool that lets us find quick solutions to some probability problems that would otherwise require solving terrifying systems of equations.
Date: Wednesday, 1/19/22, 5:40-6:40PM
Location: Zoom
Speaker: John Voight
Bio: John Voight is a professor of mathematics at Dartmouth College, where he specializes in arithmetic algebraic geometry and number theory.
Title: Quaternions
Abstract: Quaternion algebras arose from Sir William Rowan Hamilton's attempts to understand rotations in three dimensional space, but they turn up naturally across mathematical domains. Indeed, wherever you see matrices of size two by two, quaternions are lurking too! In this talk, we will give a broad survey of quaternions, including some applications. You can read his book on quaternions here.
Date: Wednesday, 12/8/21, 5:40-6:40PM
Location: Porter Hall 100 or Zoom
Speaker: Vivian Kuperberg
Bio: Vivian is currently a fifth year graduate student at Stanford University studying analytic number theory under Soundararajan.
Title: On pseudo-polynomials
Abstract: Every polynomial f with integer coefficients has the following useful property: for every integers n and k, f(n+k) is congruent to f(k) mod n. To say this a different way, f is well-defined mod n for every n. This talk will be about pseudo-polynomials, which are arbitrary functions on the integers that satisfy this same property. All polynomials are pseudo-polynomials, but it turns out there are many more: for example, floor(e*n!) is a pseudo-polynomial. We'll discuss the history of pseudo-polynomials, outstanding open questions about pseudo-polynomials, and ways to construct pseudo-polynomials that are very poorly behaved.
Date: Wednesday, 12/1/21, 5:40-6:40PM
Location: Porter Hall 100 or Zoom
Speaker: Irene Fonseca
Bio: Prof. Fonseca is a University Professor at CMU and is also the director of our very own Center for Nonlinear Analysis. Her research in pure analysis, specifically the calculus of variations, has been applied in a variety of fields, such as materials science and image processing.
Title: Mathematics and Imaging Science
Abstract: Have you ever thought that mathematical analysis and computer science are two very disjoint fields? What about topology and machine learning? All of these fields are more interconnected than you might think. In this talk we will address the mathematical treatment of image processing, including inpainting, recolorization, denoising, and machine learning schemes.
Date: Wednesday, 11/17/2021, 5:40-6:40PM
Location: Porter Hall 100 or Zoom
Speaker: Professor Adam Bjorndahl
Title: An Introduction to Knowledge Representation and Reasoning
Abstract: Formal mathematical models of knowing, learning, and communicating are useful in a variety of fields, including computer science (e.g., for reasoning about distributed systems), economics (e.g., for characterizing game-theoretic notions of strategic equilibria), linguistics (e.g., for representing semantic context and the presuppositions under which discussions take place), and philosophy (e.g., for formalizing the relationship between knowledge, belief, and justification and assessing the force of skeptical arguments). In this talk we'll motivate and explore a simple but versatile class of models for representing knowledge in both single- and multi-agent settings, paying special attention to the concept of "common knowledge". Time permitting we'll also discuss some extensions of these basic models to include dynamic representations of learning and evidence. No prior experience with these concepts/models is assumed.
Date: Wednesday, 11/3/2021, 5:40-6:40PM
Location: Porter Hall 100 or Zoom
Speaker: Kayla Wright
Bio: Kayla is a Ph.D. candidate at the University of Minnesota interested in algebraic combinatorics and representation theory!
Title: An Introduction to Schubert Calculus
Abstract: I will be giving a brief introduction to a subject called Schubert Calculus!
How many lines pass through two points in the plane? How many points do a line and a conic intersect in? And given four lines drawn randomly in three-dimensional space, how many lines intersect all four of them?
These are classical problems in enumerative geometry, the study of counting the intersection points of geometric objects. We will talk about classical ways these were thought of and also introduce modern-day ways of thinking about these problems using combinatorics of tableaux.
Date: Wednesday, 10/27/2021, 5:40-6:40PM
Location: Porter Hall 100 or Zoom
Speaker: Professor Boris Bukh
Title: You do not have to believe in transcendental numbers
Abstract: The transcendental numbers are the atoms of the number line --- they are everywhere, but few have seen one. No longer you will have to believe in the existence of these half-mythical numbers! I will arm you with the knowledge that will enable you to write a number down, and prove to your cat that it is transcendental!
Date: Wednesday, 10/20/2021, 5:40-6:40PM
Location: Porter Hall 100 or Zoom
Speaker: Professor Robin Neumayer
Title: An Introduction to Shape Optimization Problems
Abstract: In this talk, we introduce two classical shape optimization problems. The first is the isoperimetric inequality, which says that balls have the smallest perimeter among sets of a given volume. This is a mathematical reason why soap bubbles are round, as they take the shape of minimal surface area. Next, we will discuss the Faber-Krahn inequality, which says that among all drum heads of a fixed area, a circular drum produces the vibration of lowest frequency. Finally, we will discuss connections between these two shape optimization problems.
Date: Wednesday, 10/13/2021, 5:30-6:30PM
Location: Porter Hall 100 or Zoom
Speaker: Dr. Eric Stubley
Title: Solving Equations with Origami
Abstract: I'll show you how to use origami to calculate roots of any (rational) cubic polynomial! To understand why this procedure works we'll only need to know about similar triangles, but along the way we'll encounter some principles from abstract algebra and algebraic geometry that help illuminate what's really going on. I'll weave in some of the history of the mathematics of paperfolding as well. A talk about origami wouldn't be complete without some actual paper folding, so bring a blank piece of paper and a writing implement for some short activities.
Date: Wednesday, 9/29/2021, 5:30-6:30PM
Location: Porter Hall 100 or Zoom
Speaker: Dr. Tomasz Tkocz
Title: Extremal-volume projections of the cross-polytope
Abstract: To give a flavour of certain problems in high dimensional convex geometry, I shall discuss extremal-volume projections of the cross-polytope onto hyperplanes and present a beautiful solution using probabilistic and analytic ideas such as decoupling. Only knowledge about R^n is required.
Date: Wednesday, 9/23/2021, 5:30-6:30PM
Location: Porter Hall 100 or Zoom
Speaker: Dr. John Mackey
Title: I am in disarray, also Ramsey Theory
Abstract: This is mostly for new(er) members, I'll talk about a subject called Ramsey Theory, which is the art of finding structure that must exist even within the most random objects. It will just be fun.
Date: 5:40-6:40pm on Wednesday 4/6
Location: HOA 160
Speaker: Francesca Zaffora Blando
Bio: Francesca is a logician in CMU's Philosophy department, whose research intersects probability theory, information theory, and computability theory.
Title: Algorithmic randomness and Bayesian epistemology
Abstract: In this talk, I will provide an informal introduction to the theory of algorithmic randomness—a branch of computability theory that specifies what it means for an individual mathematical object (such as a real number or a binary sequence) not to display any algorithmically detectable regularities. Then, I will argue that algorithmic randomness has fruitful philosophical applications. In particular, I will show that algorithmic randomness can be used to shed light on Bayesian convergence to the truth, a phenomenon of fundamental importance to Bayesian epistemology (a probabilistic theory of rational learning).
Date: 5:40-6:40pm on Wednesday 4/27
Location: HOA 160
Speaker: Edward Hou
Bio: Edward is an undergrad at CMU interested in mathematical logic and its applications!
Title: Proofs without words, Banach–Tarski, and Circle Squaring
Abstract: We investigate the problem of given two arbitrary shapes, can one find a finite partition of one shape, so as to move around the pieces and recombine into a partition of the other shape. A celebrated 2022 result by Máthé–Noel–Pikhurko says that one can "Circle the Square" with geometrically very simple pieces. We decompose their proof into several fundamental components, revealing key insights from algebra, combinatorics, and analysis. Along the way we find old friends such as the Pythagorean theorem and the Banach–Tarski paradox.
Speaker: John Mackey
Time: 5:30 PM on Wednesday, November 6th, 2019
Location: *** HOA 160 ***
Description: Keller's conjecture is a 90 year old cube tiling conecture. I'll talk about how we recently resolved the last open case in dimension seven, aided by the computer.
Speaker: Math Club Members
Time: 5:30 PM on Wednesday, October 23rd, 2019
Location: Porter Hall 100
Description: Do you want to do something this summer? Do you want a research position, an internship, or a summer job, but don't know which one is for you or how to apply? Thankfully, Math Club can help! We will be having a panel of students with a variety of summer experiences waiting to be grilled about everything they did this summer.
Speaker: Trajan Hammonds
Time: 5:30 PM on Wednesday, October 9th, 2019
Location: Porter Hall 100
Abstract: In late 2013, Yitang Zhang and James Maynard each independently made a spectacular breakthrough in the study of prime numbers. They proved that there are bounded gaps between primes, i.e. as you go further out along the number line, you will never stop finding pairs of primes that are a bounded distance apart. In 2014, Maynard and Kevin Ford, Ben Green, Sergei Konyagin, and Terence Tao tackled the reverse question answering Erdos' most expensive prize problem: if one looks at a finite list of numbers what does the largest prime gap look like? In this talk we will survey the history of such results on gaps between primes. Motivated by recent (2019) work of William Banks, Ford, and Tao, we will discuss the limitations and advantages of using probabilistic models to study the primes, resulting in heuristics for large gaps between primes and the Twin Prime Conjecture. We will answer such questions as, "Why is the Riemann Hypothesis true with probability 1?" and "What do spacings between primes have to do with wait times for the next 71B?" Time permitting we will discuss some open problems.
Speaker: Nicolas Naing
Time: 5:30 PM on Wednesday, October 2nd, 2019
Location: ***Margaret Morrison 103***
Abstract: My resarch over the summer focused on random generation methods for binary trees. This process is used to reduce the number of trees cross-compared in finding the expected number of edges in common between two randomly selected trees of a given size n. My work implemented three methods: the first method, which generates the tree from left to right, the Yule method, which generates a tree by randomly selecting nodes, and the Remy method, which generates a tree by randomly selecting edges. All of these trees were implemented using recursion and some probability concepts (Bayes' rule). Each method has its own advantages in terms of runtime and implementation, but coding all three has helped me fine tune my recursion skills and casework, which will be useful in later math research.
Speaker: Chris Grossack
Time: 5:30 PM on Wednesday, September 25th, 2019
Location: Porter Hall 100
Abstract: Say you're writing a videogame, or running a game of Dungeons and Dragons, and you want your players to be lost in a dungeon of some kind. Being a mathematically inclined person, you decide it would be fun (for certain definitions of fun) to base your dungeon's layout on a group. Shockingly, if you choose a bad group, it is impossible to know if your players reached the exit or not! In a lighthearted introduction to geometric and combinatorial group theory, we will talk about why we provably can't know if we're at the exit, and will discuss exactly how unlucky you have to be to get one of these "bad groups" at random. Time permitting, we will talk about some algorithms for deciding where the exit is in specific cases.
Speaker: Jo Ellis-Mohaghan
Time: 5:30 PM on Wednesday, September 18th, 2019
Location: Porter Hall 100
Abstract: Applications of immediate concern have driven some of the most interesting questions in the field of graph theory, for example graph drawing and computer chip layout problems, random graph theory and modeling the internet, graph connectivity measures and ecological systems, etc. Currently, scientists are engineering self-assembling DNA molecules to serve emergent applications in biomolecular computing, nanoelectronics, biosensors, drug delivery systems, and organic synthesis. Often, the self-assembled objects, e.g. lattices or polyhedral skeletons, may be modeled as graphs. Thus, these new technologies in self-assembly are now generating fascinating and challenging new design problems for which graph theory is a natural tool. We will present some new applications in DNA self-assembly and describe some of the graph-theoretical design strategy problems arising from them. We will see how finding optimal design strategies leads to developing new algorithms for graphs, addressing new computational complexity questions, and finding new graph invariants corresponding to the minimum number of components necessary to build a target structure under various laboratory settings. This is a rich area for open problems, interdisciplinary collaborations, and involvement for all levels of investigators, especially students.
Speaker: Chloe Ireland
Time: 5:30 PM on Wednesday, September 11th, 2019
Location: Porter Hall 100
Description: Consider a graph, G, and a ring, R. Create a function p: V \cup E \to R as follows: first, label the edges of our graph with ideals from R. Then, label each vertex with an element of R in such a fashion so that if an edge e = uv \in E, p(u) - p(v) = p(e). This graph labeling through the function p is called a graph spline. In this talk, I examine the generalized graph splines introduced by Gilbert, Tymoczko, and Viel and focus on an attribute known as the Universal Difference Property (UDP). If u and v are arbitrary vertices in our graph, UDP determines the set in which p(u) - p(v) is contained. I will show some simple graphs where UDP is satisfied, as well as show that UDP is a structural property of edge labeled isomorphic graphs. Finally, I will conclude by mentioning the concept of Prufer domains to illustrate that not every edge labeled graph satisfies UDP.
Speakers: A panel of students!
Time: 5:30 PM on Wednesday, May 1st, 2019
Location: Porter Hall 100
Description: Come listen to different graduating seniors talk about their application experiences! We'll have some prewritten questions and introductions and then open up the floor to even more questions afterward. Come find out how to apply for grad programs, interview tips, visiting, and more!
Speaker: Vipul Goyal
Time: 5:30 PM on Wednesday, April 24th, 2019
Location: Porter Hall 100
Description: Suppose you have been able to prove that P=NP. However, you are wary of sharing your proof with others since they might steal it and claim the million dollar prize. Can you convince others of this fact without revealing your proof? In general, can you prove a statement to a verifier without revealing anything about the proof or the witness? It turns out that this is possible for almost any statement that one can think of. In this talk, we will dive into fascinating objects called zero-knowledge proofs which allow a prover to prove to a verifier that a statement is true without revealing anything else (except its validity). We will also see how anything which is provable is also provable in zero-knowledge.
Speakers: Math Club Members and Faculty
Time: 5:30 PM on Wednesday, April 17th, 2019
Location: Porter Hall 100
Description: Want to hear from another student whether a certain course or instructor is as great as you expect? This is the best opportunity to ask fellow math majors questions regarding the content, quality, and general experience of the various courses and instructors in the math department. No faculty will be present (with the exception of Prof. Howell for the first 5-10 minutes), so students should feel free to be open and honest about their experiences.
Speaker: Kristopher Lee
Time: 4:30 PM on Friday, April 5th, 2019
Location: Doherty Hall 2210
Description: The Mathematical Sciences Department is in the process of hiring a new member of the Teaching Track faculty at CMU. Each of four candidates will give a special Math Club Colloquium talk that showcases their research at an undergraduate level. Each of the colloquia will last an hour and be followed by a reception.
Speaker: David Offner
Time: 4:30 PM on Wednesday, April 3rd, 2019
Location: Doherty Hall 2210
Description: The Mathematical Sciences Department is in the process of hiring a new member of the Teaching Track faculty at CMU. Each of four candidates will give a special Math Club Colloquium talk that showcases their research at an undergraduate level. Each of the colloquia will last an hour and be followed by a reception.
Speaker: Clive Newstead
Time: 4:30 PM on Friday, March 29th, 2019
Location: Doherty Hall 2210
Description: The Mathematical Sciences Department is in the process of hiring a new member of the Teaching Track faculty at CMU. Each of four candidates will give a special Math Club Colloquium talk that showcases their research at an undergraduate level. Each of the colloquia will last an hour and be followed by a reception.
Speaker: Mary Radcliffe
Time: 4:30 PM on Wednesday, March 27th, 2019
Location: Doherty Hall 2210
Description: The Mathematical Sciences Department is in the process of hiring a new member of the Teaching Track faculty at CMU. Each of four candidates will give a special Math Club Colloquium talk that showcases their research at an undergraduate level. Each of the colloquia will last an hour and be followed by a reception.
Speaker: Joshua Siktar
Time: 5:30 PM on Wednesday, March 20th, 2019
Location: Porter Hall 100
Abstract: An introductory course in numerical methods typically devotes substantial attention to analyzing algorithms for finding roots of functions $f\in C^0(\mathbb{R}).$ One of the most frequently asked questions is how to find an optimal starting point for your algorithm of choice. In this article we explore a related question: if we don't know how to find a good starting point, then how many iterations of an algorithm are we expected to make in order to guarantee our error is below a certain threshold? We explore the answer to this question for linearly convergent algorithms, using a method that we aptly call the Random Initial Points Technique.
Speaker: Maria Chikina
Time: 5:30 PM on Wednesday, March 6th, 2019
Location: Porter Hall 100
Abstract: Matrix factorization features in many high dimensional data analysis problems. Typically, factorization methods are used to reduce the dimensionality of data and to visualize its structure. Factorization methods can also be viewed as models for whatever process is actually generating the data represented by the matrix. However, unlike for dimensionality reduction or visualization, success at this third goal is highly dependent on the specific factorization technique used. We will discuss a method that uses weak prior knowledge constraints to obtain interpretable matrix factorizations of biological data.
Speaker: Chris Grossack
Time: 5:30 PM on Wednesday, February 27th, 2019
Location: Porter Hall 100
Abstract: Formal logic, in particular Godel's completeness theorem, provides a flexible technique for quickly turning finite combinatorial results into infinite generalizations with almost no work at all. In this talk we will explore Logical Compactness and some of its combinatorial applications.
Speaker: Franziska Weber
Time: 5:30 PM on Wednesday, February 20th, 2019
Location: Porter Hall 100
Abstract: Braess's paradox is a proposed explanation for when the modification of a road system by for example adding a new road, leads to a worse traffic situation instead of an improvement. It was proposed in 1968 by the mathematician Dietrich Braess and can mathematically be formulated as a Nash Equilibrium that is a worse situation than the best overall flow through the road network. In this talk, we review Braess's paradox and its emergence in many real life situation and then explore whether it can be observed in traffic flow models involving partial differential equations.
Speaker: Dejan Slepcev
Time: 5:30 PM on Wednesday, February 13th, 2019
Location: Porter Hall 100
Abstract: Over 200 years ago Monge wondered what is the most efficient way to transport a pile of sand to fill in a given hole given that the cost of transporting a unit mass from its initial to final location is equal to the distance between them. About 10 years later Kantorovich realized how to reformulate the problem to show that it has a form of a solution. Works of Brenier, as well as others, have explained precisely what is the form of the transport is. We will discuss the optimal transportation problem and some of its applications.
Speaker: Dr. Irina Gheorghicuic and Dr. Jason Howell
Time: 5:30 PM on Wednesday, February 6th, 2019
Location: Porter Hall 100
Abstract: Dr. Irina Gheorghicuic and Dr. Jason Howell will discuss undergraduate research in mathematical sciences at CMU and beyond. They will describe what an undergraduate research project usually entails and how to search for opportunities. They will also discuss how to apply for summer programs and grants, highlighting important aspects of application materials. Some students who have participated in summer research in the past will share their experiences as well.
Speaker: Tomasz Tkocz
Time: 5:30 PM on Wednesday, November 28th, 2018
Location: Porter Hall 100
Abstract: How many planks of width one foot each do you need to cover a circular tabletop of diameter n feet? We shall present Bang's solution to a generalization of this problem for convex sets and discuss related open problems.
Speaker: Alan Frieze
Time: 5:30 PM on Wednesday, November 14th, 2018
Location: Porter Hall 100
Abstract: A walker traverses a graph step by step. Between steps, an adversary deletes edges. We study variants on this game where the walker's goal is to visit as many vertices as possible. Joint with Lisa Espig, Micahel Krivelevich, Wesley Pegden.
Speakers: Math Club Members and Faculty
Time: 5:30 PM on Wednesday, November 7th, 2018
Location: Porter Hall 100
Description: Want to hear from another student whether a certain course or instructor is as great as you expect? This is the best opportunity to ask fellow math majors questions regarding the content, quality, and general experience of the various courses and instructors in the math department. No faculty will be present (with the exception of Prof. Howell for the first 5-10 minutes), so students should feel free to be open and honest about their experiences.
Speaker: Anton Bernshteyn
Time: 5:30 PM on Wednesday, October 31, 2018
Location: Porter Hall 100
Abstract: In 1924, Stefan Banach and Alfred Tarski showed that it is possible to cut a pumpkin into finitely many pieces, move the pieces around, and make two pumpkins that are perfectly identical to the original one. In this spooky talk, we will explore this result, known as the Banach-Tarski paradox, and discuss some related recent research.
Speaker: Florian Frick
Time: 5:30 PM on Wednesday, October 24, 2018
Location: Porter Hall 100
Abstract: In 1911 Otto Toeplitz conjectured that any simple closed curve in the plane inscribes a square. I will survey some of the results towards this conjecture, which still remains open, and talk about variants of this question for curves in higher dimensions. For example, does every simple closed curve in 3-space inscribe a parallelogram? Surprisingly, these problems are related to the question whether a group of thieves can fairly divide a necklace. I will explain this connection.
Participants: You!
Time: 9:00 PM on Wednesday, October 17, 2018
Location: Baker Hall A51 (Giant Eagle Auditorium)
Description: This is a joint event between the CMUMC and University of Pittsburgh's Math Club! Join us for a fun and chill hour of math trivia and - of course - pizza.
Speaker: James Cummings
Time: 5:30 PM on Wednesday, October 10, 2018
Location: Porter Hall 100
Abstract: I'll begin with a discussion of "fast growing functions." Then I'll show they can be used to produce examples of theorems in finite combinatorics which can't be proved without appeals to infinity.
Speaker: David Altizio
Time: 5:30 PM on Wednesday, October 3, 2018
Location: Wean Hall 5403
Abstract: The world of contest mathematics is wondrous but strange. Contestants are presented with a variety of questions to solve, and some of them push the boundaries of pre-calculus mathematics in jaw-dropping ways. The creation of these questions is somewhat of a mystery though, as the inspirations behind contest questions are rarely shared to the public. In this talk, I will attempt to demystify this cloudiness a bit by exploring my seven-year-long journey through problem writing. In particular, I will discuss common writing techniques, sources of inspiration, and the stories behind some of my favorite creations.
Speakers: A panel of students!
Time: 5:30 PM on Wednesday, September 19, 2018
Location: ***Doherty Hall A302***
Description: Come listen to different undergrads talk about their internship and research experiences! We'll have some prewritten questions and introductions and then open up the floor to even more questions afterward. Come find out how we applied for the internships, interview tips, TOC experiences, and more!
Speaker: Trajan Hammonds
Time: 5:30 PM on Wednesday, September 12, 2018
Location: Porter Hall 100
Abstract: In this talk we will discuss the importance of error terms in number theory, from estimating the number of primes up to a given height to counting the number of ways you can write a positive integer as the sum of twenty four squares. In our journey we will learn about the celebrated Riemann Hypothesis and other famous conjectures in number theory and why they're so powerful. Time permitting, we will discuss research from this past summer on the Sato-Tate conjecture for primes in arithmetic progressions. This talk is inspired by Barry Mazur's BAMS paper of the same name.
Speaker: Seniors!
Time: 5:30 PM on Wednesday, May 2nd, 2018
Location: Porter Hall 100
Description: Get pumped for a fun post-Booth panel about grad school with our very own Math Club seniors and plenty of cake!
Speaker: Mike Gaal
Time: 5:30 PM on Wednesday, April 25th, 2018
Location: Porter Hall 100
Description: Mike Gaal is a 1997 CMU graduate with a degree in Math (Operations Research concentration) who is currently a Principal and Consulting Actuary at Milliman in Chicago. He will give a high-level overview of an actuarial career and discuss some of his personal experiences as a CMU math graduate. If you are a math major who would like to learn more about what an actuary does and how to become one, then this is a unique opportunity for you to get to know an actuary and ask him for advice.
Speaker: Clinton Conley
Time: 5:30 PM on Wednesday, April 18th, 2018
Location: Porter Hall 100
Abstract: The pigeonhole principle on the natural numbers can be stated as follows: if you color each natural number red or blue, one of the two colors contains a "copy" of the natural numbers. The infinite Ramsey theorem can be thought of as a high dimensional analog of this, coloring pairs or triples instead of single numbers. We can make this a bit more precise, and discuss how the picture changes for different linear orders (the rationals play a starring role, but the reals and ordinals may make guest appearances).
Speakers: Math Club Members and Faculty
Time: 5:30 PM on Wednesday, April 11th, 2018
Location: Porter Hall 100
Description: Want to hear from another student whether a certain course or instructor is as great as you expect? This is the best opportunity to ask fellow math majors questions regarding the content, quality, and general experience of the various courses and instructors in the math department. No faculty will be present (with the exception of Prof. Howell for the first 5-10 minutes), so students should feel free to be open and honest about their experiences.
Speaker: Boris Bukh
Time: 5:30 PM on Wednesday, April 4th, 2018
Location: Porter Hall 100
Abstract: Reliable communication is difficult. Street noise drowns the words from a friend. Oceans swallow messages in bottle from shipwreck survivors. The radio signals from nearby stars are lost amidst the cacophony of space. And there is bad handwriting. I will explain about ways to make communication more reliable. The focus will be on completely error-free communication. We will see some graphs and a little bit of linear algebra. An example of bad handwritting will be provided.
Speaker: Po-Shen Loh
Time: 5:30 PM on Wednesday, March 28th, 2018
Location: Porter Hall 100
Abstract: It's easy to generate large numbers for their own sake. A more interesting question is whether huge numbers ever arise naturally from simple-looking situations. In this talk, we will explore two examples of this phenomenon. The first will be a surprise from the International Mathematical Olympiad. The second concerns Szemeredi's Regularity Lemma, a result of central significance in graph theory.
Speaker: Christopher Perry
Time: 5:30 PM on Wednesday, March 21st, 2018
Location: Porter Hall 100
Abstract: Have you ever cut out a chain of paper figures or hearts? Or perhaps, what shapes you could make with fewer cuts? The Fold and Cut Problem asks what shapes can be created by folding a piece of paper, and creating a single cut through it. This talk will include the discussion of several methods and approaches to solving this problem, related theorems in paper folding, and some activities surrounding folding and cutting paper. Please bring scissors if you have them!
Speaker: Jason Howell
Time: 5:30 PM on Wednesday, March 7th, 2018
Location: *** Wean Hall 7500 ***
Abstract: The performance of direct solvers for large, sparse linear systems of equations depends on a symbolic factorization of the coefficient matrix, which employs graph algorithms and data structures to determine the amount of work and memory required to factor the matrix. The location of the nonzero entries can heavily influence the symbolic factorization, and the presence of a dense row in the matrix can lead to significant overestimates of the amount of memory and work required to complete the factorization. In this talk we describe how an unconfentional application of a null space method for saddle point problems can be utilized to eliminate small number of dense rows while preserving the overall sparsity of the matrix. This results in a prestructuring technique, i.e. a method that seeks to modify the nonzero structure of the matrix with the intent of realizing gains in direct solver performance.
Talk Slides: Click here.
Speaker: Alp Muyesser
Time: 5:30 PM on Wednesday, February 28th, 2018
Location: *** Doherty Hall 1212 ***
Abstract: Combinatorial chaos is everywhere: whether we are trying to bound Ramsey numbers, compute NP-hard languages, or solve complex board games like Go, we have to deal with the fact that 2^x grows, really, really fast. But chaos can also arise in way simpler settings, say when we are merely picking up stones from a bunch of piles! We'll discuss how we came really close to a complete characterization of an embarrassingly simple Nim-like impartial game, yet how combinatorial chaos managed to elude us once again. This is a very active and accessible area of research. All you need to know is how induction and binary works! This is joint research with Calvin Beideman and Matt Bowen.
Speaker: Dr. April Galyardt
Time: 5:30pm on Wednesday, February 21st, 2018
Location: *** Doherty Hall 2315 ***
Information: Dr. Galyardt is a statistician and data scientist at Carnegie Mellon University's Software Engineering Institute. She received her PhD from Carnegie Mellon University's Statistics Department, but received her Bachelor's and Master's in Mathematics previously. In Fall 2017, she taught 36-401 Modern Regression at CMU. She will speak on the modeling of cognition, and how interdisciplinary collaboration plays a role in learning and beyond.
Activity: Games and heart-shaped pizza!
Time: 5:30 PM, Wednesday, February 14, 2018
Location: Porter Hall 100
More Information: What an amazing coincidence! Valentine's Day has fallen on the day of a Math Club meeting! Come join most of exec for an exciting hour of games and thematically appropriate pizza - feel free to bring your own games as well.
Movie: N is a Number: A Portrait of Paul Erdos
Time: 5:30 PM, Wednesday, February 7, 2018
Location: Porter Hall 100
More Information: 2/7/18 is e Day (for the beloved mathematical constant, e=2.718...), and what better way to celebrate than with a movie about a certain mathematician whose name starts with the letter e - Erdos (sorry Euler)! This critically acclaimed movie is 57 minutes long and rated 7.5/10 on IMDb. There will also be plenty of Pittsburgh Popcorn to go around! Happy e Day!
Speaker: Professor John Mackey
Time: 5:30pm on Wednesday, January 31, 2018
Location: Porter Hall 100
Abstract: When n people play each other in a tournament (each person playing the other n-1 people), we'd like to rank the participants after knowing the results. Cycles are an impediment to such a ranking. If A beats B, B beats C, and C beats A, how should A, B, and C be ranked relative to one another? I will explain just how many of these cycle impediments can exist in a tournament (for 3, 4, and 5 cycles), and then state some open problems related to this question. This is joint work with Natasha Komarov.
Speaker: Professors Jason Howell and Irina Gheorghiciuc
Time: 5:30pm on Wednesday, November 29th, 2017
Location: Porter Hall 100
Slides : Here.
Abstract: During this meeting, Dr. Irina Gheorghiciuc and I will give a presentation about undergraduate research opportunities in mathematical sciences at CMU and beyond. We will describe what an undergraduate research project usually entails and how to search for opportunities. We will also discuss how to apply for summer programs and grants, highlighting important aspects of application materials. Some students who have participated in summer research in the past will share their experiences as well.
Speaker: Professor Ian Tice
Time: 5:30pm on Wednesday, October 25th, 2017
Location: Doherty Hall A302
Abstract: Until the 19th century it was widely believed among mathematicians that continuous functions of a real variable should in fact be differentiable at "most" points. It thus came as quite a surprise when Karl Weierstrass constructed a beast of a continuous function that is differentiable nowhere. The purpose of this talk is to construct such a monstrous function.
Speaker: Professor Kate Thompson, Visiting Shelly Professor
Time: 5:30pm on Wednesday, October 11th, 2017
Location: Porter Hall 100
Abstract: One of the most classic results in number theory was originally stated by Fermat in a letter to Mersenne dated Christmas,1640. In "typical" Fermat fashion, the first proof didn't appear for over 100 years. Having said that, this result shows the breadth and beauty of number theory techniques. Time permitting, we will go through a (1) algebraic (2) geometric (3) analytic proof of this result. At the end, we will also discuss generalizations of this result, some proved as recently as 2013.
Talk Slides: Click here.
Speaker: Michael Spoerl, Senior Math Major
Time: 5:30pm on Wednesday, September 27th, 2017
Location: Porter Hall 100
Abstract: In a 2002 paper, Brezis gave a (relatively) simple criterion for identifying constant functions. The proof, however, is not so simple - it requires a detour through Sobolev spaces. In this talk I will introduce the theory of Sobolev spaces and use the main theorem of Brezis' paper to prove his criterion. Only a conceptual understanding of calculus is needed.
Time: 5:30pm on Wednesday, September 20th, 2017
Location: Porter Hall 100
Details: The Mathematical Contest in Modeling (MCM) is a yearly contest for undergraduates interested in applied mathematics- think of it like a cross between Putnam and a hack-a-thon for math. A team has 96 hours to put together a solution to a problem in math modeling. Some examples of problems from the past:
Estimate the global effects of a large asteroid impacting Antarctica
Study the hunting strategies of velociraptor dinosaurs based on fossil data
Develop a more efficient method of boarding passengers onto large commercial jets
If this sounds interesting to you, feel free to email Adrian Hagerty (Math Grad student, president of SIAM).
Time: 5:30pm on Wednesday, September 13th, 2017
Location: Porter Hall 100
Details: Welcome to Math Club! We'll introduce ourselves, give a brief overview of the type of things we do, show a tentative schedule of our events this weekend, and advertise our first event: Going to a Pirates Game on Friday, September 22nd! If we have time, we'll wrap up by watching the short film Flatland . There will be Pizza!
Speaker: Giovanni Leoni, Professor of Mathematics, CMU
Time: 5:30pm on Wednesday, April 12th, 2017
Location: Doherty Hall 2315
Abstract: In this talk I will try to motivate the notion of viscosity solutions for ordinary differential equations.
Speaker: Josh Laison, Associate Professor of Mathematics, Willamette University
Time: 5:30pm on Monday, Mar. 27th, 2017
Location: Scaife Hall 125
Abstract: We discuss a new variation of a 400-year-old problem from Johannes Kepler and Isaac Newton about how densely geometric shapes can be packed together. Along the way we'll encounter Amazon delivery robots, geometric networks, an iPhone game, computers that prove theorems, 24-dimensional spheres, Tetris, cannonballs, and some exciting new theorems. Joint work with Andrew Bishop, Ben Gardiner, and David Livingston.
Speakers: Joseph Zoller and Ani Sridhar, Juniors at CMU
Time: 5:30pm on Wednesday, Mar. 8th, 2017
Location: Margaret Morrison 103
Abstract: We will explore the basic notions in real analysis such as continuity, differentiability and integrability and completely annihilate any intuition you may have about them. We'll use and introduce basic tools from real analysis to construct strange functions. Memes will be provided.
Speaker: Liza Sulkin, Freshman Mathematics Major, CMU
Time: 5:30pm on Wednesday, Feb. 22nd, 2017
Location: Doherty Hall 2315
Abstract: Fermi Questions involve quickly determining the order of magnitude of absurd questions. We'll be answering several important questions such as:
How many Cathedral of Learnings would it take to reach Philadelphia from Pittsburgh?
How many wire cuts would it take to free the UC Stones?
Speaker: Nicholas Hoell, University of Toronto
Time: 4:30pm on Friday, Feb. 3rd, 2017
Location: Wean 7500
Abstract: We will explore the mathematics of the attenuated ray transform. The problem of recovering an unknown function based on measuring its weighted line integrals arose in medical imaging modalities and is connected to deep open questions in geometry. Some of the techniques used to address this problem involve ideas from harmonic analysis, representation theory, and gauge theory. No background knowledge of these fields or of inverse problems in medical imaging is assumed.
Speaker: Jason Howell, College of Charleston
Time: 4:30pm on Friday, Jan. 27th, 2017
Location: Wean 7500
Abstract: In this talk we will survey several different applications of differential equations in a variety of settings. Witha primary focus on the modeling process and the influence of problem parameters on solutions, we will discuss how basic mathematical models of population growth and interaction can be extended to a multitude of areas, including love affairs, the spread of communicable diseases, warfare and combat, marketing, the spread of ideas, and even a zombie apocalypse. I will also discuss some ongoing undergraduate research projects that focus on popularity dynamics and targeted advertising. If time permits, a brief discussion of some applications of partial differential equations will be discussed.
Speaker: Boris Bukh, Associate Professor of Mathematics, CMU
Time: 5:30pm on Wednesday, Nov. 16th, 2016
Location: Gates 4307
Abstract: All over the globe, young school children spend millions of hours multiplying numbers. I will demonstrate possible ways of multiplying numbers. While much improvement is possible, they offer no relief to the children. I will conclude the talk with cryptic remarks about college students multiplying matrices.
Speaker: Zachary Singer, Junior Mathematics Major, CMU
Time: 5:30pm on Wednesday, Oct. 19th, 2016
Location: Wean 7500
Abstract: What does a butterfly flapping its wings have to do with the Triforce? In this talk we introduce a few ideas of chaos theory and fractal geometry, as well as how different notions of dimension can lead to a set having non-integral dimension. These ideas can be combined to help determine the behavior of how a biological virus spreads, which is one application I worked with over the summer.
Speaker: Misha Lavrov, Mathematics PhD Student, CMU
Time: 5:30pm on Wednesday, Oct. 5th, 2016
Location: Gates 4307
Abstract: Click here for a pdf version.
Talk Slides: Click for slides in a pdf version.
Speaker: Sam Zbarsky, Senior Mathematics Major, CMU
Time: 5:30pm on Wednesday, Sept. 21st, 2016
Location: Gates 4307
Abstract: This talk will be an introduction to two tools useful in studying partial differential equations: the Fourier transform and energy methods. I will introduce both of them, and show how they apply to several partial differential equations, including one I worked with over the summer.
Speaker: Niraj Khare, Faculty Candidate for CMU Qatar
Time: 5:00pm on Wednesday, Mar.23rd, 2016
Location: DH 2315
Abstract: Click here for a pdf version
Talk Slides: slides in pdf version
Speaker: Zijian Diao, Faculty Candidate for CMU Qatar
Time: 5:00pm on Wednesday, March 2nd, 2016
Location: DH 2315
Abstract: Is sine of 1 degree rational? At a glance this question seems light years away from quantum computing, a cutting-edge research area where computer science meets quantum mechanics. Surprisingly, this question matters not only in the mathematical world, but also in the quantum realm. Its answer and many other rudimentary facts of trigonometry have found their way into the study of various research problems in quantum computing. In this talk we will explore these intriguing connections through the interplay of quantum algorithms and topics from number theory and classical analysis. Along the way, we will solve a long-standing puzzle in quantum search and provide a quantum approach to the centuries-old Basel problem.
Speaker: Martin Juras, Faculty Candidate for CMU Qatar
Time: 5:00pm on Wednesday, Feb.24th, 2016
Location: WEH 8220
Abstract: Click here for a pdf version
Speaker: Adrian Hagerty, PhD student in Math Dept at CMU
Time: 5:30pm on Wednesday, Feb.17th, 2016
Location: DH 2315
Abstract: The study of Functional Analysis forms an important role in the modern fields of PDEs and Calculus of Variations. This involves taking the familiar notion of a vector space and bringing it to the realm of infinite dimensions. What new problems arise as we attempt to generalize our old tools to the infinite setting?
Speaker: Clive Newstead, PhD student in Math Dept at CMU
Time: 5:30pm on Wednesday, Jan.27th, 2016
Location: DH 2315
Abstract: The idea of equipping a set with a structure is ubiquitous in mathematics. For example, graphs are sets equipped with an edge relation, groups are sets equipped with an algebraic structure, topological spaces are sets equipped with a notion of openness, posets are sets equipped with a notion of order... the list goes on forever and ever and ever. This talk will introduce a candidate for defining 'structure' in the abstract. With the tools we develop, we can prove some pretty cool stuff in enumerative combinatorics.
Speaker: Peter Winkler, William Morrill Professor of Mathematics and Computer Science, Dartmouth
Time: 5:30pm on Wednesday, Dec.2nd, 2015
Location: DH 1112
Abstract: Supposedly our intuition about probability---even though humans invented the concept---is faulty. Lots of puzzles, naturally, are designed to lead us down the garden path to incorrect conclusions. But maybe our intuition is not as bad as we think. We'll take a fresh look at some paradoxes, old and new, to see whether we or our assumptions are at fault.
Poster: Poster
Speaker: Winston Yin, senior at CMU, math and physics double major
Time: 5:30pm on Wednesday, Nov.18th, 2015
Location: PH 100
Abstract: The peculiar properties of a shape-memory alloy are the result of the fine structure formed between its several crystalline forms. How do these fine structures arise from basic ideas about a crystal? In this talk, I will explain how infinitely fine structures are a natural consequence of integral minimization problems, as well as the project I worked on at Oxford this summer.
Speaker: Irene Fonseca, Mellon College of Science University Professor of Mathematics, Director of Center for Nonlinear Analysis
Time: 5:30pm on Wednesday, Nov.11th, 2015
Location: PH 100
Abstract: A plethora of physical and technological applications ranging from analyzing instabilities in materials science to image analysis in computer vision are subject to rigorous mathematical understanding through recently developed methods and articulation of ideas in the calculus of variations, geometric measure theory, and nonlinear partial differential equations. In this talk, these techniques will be used for recolorization of damaged images.
Speaker: Richard Schwartz, Chancellor`s Professor of Mathematics, Brown University
Time: 11:30 on Friday, Oct.16th, 2015
Location: WEH 8200
Speaker: Paul Raff, CMU alumus, now Principal Data Scientist at Microsoft
Time: 5:30 on Thursday, Oct.1st, 2015
Location: WEH 7500
Abstract: From Pure Math to Data Science (pptx)
Speaker: Po-Shen Loh, Math Professor at CMU, USA IMO Lead Coach
Time: 5:30 on Wednesday, Sept.30th, 2015
Location: PH 100
What's the longest sequence of triples (x1, y1, z1), (x2, y2, z2), ... that satisfies the following properties? (1) Each number is an integer between 1 and N inclusive. (2) For every j less than k, if we compare the triples (x_j, y_j, z_j) and (x_k, y_k, z_k), there are at least two coordinates in which the latter triple strictly exceeds the former triple. It turns out that this simple-sounding problem is equivalent to a question from Ramsey Theory, inspired by a question from k-majority tournaments, and related to deep question involving induced matchings and Szemeredi' s Regularity Lemma. The talk will be a tour of Combinatorics which introduces many of these concepts along the way.
Speaker: Adam Williams, senior math major at CMU
Time: 5:30 on Wednesday, Apr 29th, 2015
Location: Scaife 125
Imagine you have a finite set of particles, moving along the x axis, with fixed masses and initial velocities. When two particles collide, they *stick* together to form a new particle, preserving the mass and momentum of the original two. This is a simple set-up, but seems potentially difficult to work with mathematically. Adam shows you how you can use math to study this system in a way that makes it much more understandable.
Speaker: William Mance, PhD, CMU alumnus
Time: 5:00 on Wednesday, Apr 22nd, 2015
Location: Scaife 125
We explore in depth the theoretic and statistical properties of certain sets of numbers arising from their Cantor series expansions. As a direct consequence of our main theorem we deduce numerous new results as well as strengthen known ones. This work was coauthored with Dylan Airey while he was still a high school student at the Texas Academy of Mathematics and Science. Our main theorem will touch on issues related to computability theory, ergodic theory, fractal geometry, number theory, and probability theory.
Speaker: Steven Miller, Professor at Williams College
Time: 5:30 on Wednesday, Mar 25th, 2015
Location: Scaife 125
Many systems exhibit a digit bias. For example, the first digit base 10 of the Fibonacci numbers or of 2^n equals 1 about 30% of the time; the IRS uses this digit bias to detect fraudulent corporate tax returns. This phenomenon, known as Benford s Law, was first noticed by observing which pages of log tables were most worn from age – it is a good thing there were no calculators 100 years ago! We will discuss the general theory and application, talk about some fun examples (ranging from the 3x1 problem to the Riemann zeta function), and if time permits discuss some joint results with my REU students.
Speaker: Tomer Reiter, senior math major at CMU
Time: 5:30 on Wednesday, Mar 4th, 2015
Location: Scaife 125
The Birch and Swinnerton-Dyer conjecture is one of the Millennium Problems. The conjecture relates the group of rational points on an elliptic curve to information associated with the equation for the elliptic curve over finite fields. In the talk, we will see some of setup for the conjecture, the statement and some of the partial progress made. I will basically assume David's talk last time as a prerequisite, but I will briefly go over the facts about elliptic curves he mentioned that we will need.
Speaker: David Mehrle, senior math major at CMU
Time: 5:30 on Wednesday, Feb 18th, 2015
Location: Scaife 125
A positive integer N is called congruent if it is the area of a right triangle whose sides have rational lengths. Determining whether or not a given positive integer is congruent is a millennia-old problem that is still open today. I will explore this problem and several attempted solutions, including an interesting modern approach using elliptic curves.
Speaker: Misha Lavrov, PhD student at CMU
Time: 5:30 on Wednesday, Jan 28th, 2015
Location: Scaife 125
If you are speaking with an alien from Mars who knows a lot of math and has never heard the word Euclid, explaining what geometry is can be frustrating. You will try very hard to come up with foolproof ways to axiomatize geometry, and the alien will persist in coming up with bizarre structures that look nothing like what you imagined. In 1899, Hilbert came up with a set of 16 alien-proof axioms for plane geometry. (That is not quite true. He had 17. But there’s been some progress in the intervening century.) In this talk, I will play the role of the alien in an effort to persuade you that the task of Hilbert was not an easy one.
Speaker: Noam Elkies, Professor of Mathematics, Harvard University
Time: 5:30 to 6:30 on Wednesday, December 3rd
Location: WEH 7500
TBA
Speaker: Giovanni Leoni, Professor of Mathematics
Time: 5:30 to 6:30 on Wednesday, October 27th
Location: DH 1112
In this talk we will discuss the fundamental theorem of algebra and give an analytical proof.
Speaker: Boris Bukh, Assistant Professor of Mathematics
Time: 5:30 to 6:30 on Wednesday, October 8th
Location: DH 1112
The transcendental numbers are the atoms of the number line --- they are everywhere, but few have seen one. No longer you will have to believe in the existence of these half-mythical numbers! I will arm you with the knowledge that will enable you to write a number down, and prove to your cat that it is transcendental!
Pizza will be served.
Speaker: Po Shen Loh, Assistant Professor of Mathematics
Time: 5:30 to 6:30 on Wednesday, September 24th
Location: MM 103
This year, problem 6 on the International Math Olympiad turned out to be a semi-open research problem. The originally proposed problem is solvable using basic methods, but it is still open to determine the best possible result. A set of lines in the plane is in general position if no two are parallel and no three are concurrent. A set of lines in general position cuts the plane into cells, some of which have finite area; we call these finite cells. Prove that for all sufficiently large $n$, in any set of $n$ lines in general position it is possible to color at least $\sqrt{n}$ of the lines blue in such a way that none of its finite cells has a completely blue boundary. What's the best bound that you can get? We'll improve the stated bound using techniques from probabilistic combinatorics and extremal hypergraph theory.
Speaker: Nick Takaki, Undergraduate
Time: 5:30 to 6:30 on Wednesday, September 10th
Location: DH 1112
A biphase approximation of an image is a two-color piecewise-constant approximation of the original image which maximizes regional fidelity while minimizing complicated boundaries. When it comes to segmenting images, human intuition is very strong. We often have strong gut feelings about which pixels belong in which regions, where object boundaries should be, and what should be discounted as noise or damage. Variational image segmentation seeks to formalize these "gut feelings" by creating a functional which quantifies the error of approximation, and then defining correct segmentations as local minima of this functional. In this talk, I will discuss the intuition behind variational image approaches, popular region-based segmentation methods including the Chan-Vese model, and my group's summer research into a segmentation method which dynamically identifies artifacts and corrects shadows.
Speaker: Carson Sestili, Undergraduate
Time: 5:30 on Thursday, May 1, 2014
Location: WEH 5415
An elementary cellular automaton is a sort of computational model. States are sequences of bits. Transitions between states are specified by a simple, deterministic rule that updates each bit according to a small neighborhood around that bit in the previous state. Even though the model is simple to describe, many cellular automata have surprisingly beautiful and complicated behavior. In some cases their behavior is so unpredictable that it might be called "random," even though there is no randomness in the system. In this talk I will show why several automata exhibit chaotic behavior, for a popular definition of chaos.
Speaker: Andy Niedermaier, Jane Street Capital
Time: 5:30pm on Wednesday, March 26, 2014
Location: DH 2210
They're called Fermi problems...
how many traffic lights are there in Boston?
how many social security numbers are primes?
how many calories are in an average Cheesecake Factory?
how many times will this activity get rescheduled due to bad weather?
Jane Street presents "The Estimathon." Attempt 13 estimation problems in 30 minutes, ranging from totally trivial to positively Putnamesque. Work in teams to come up with the best set of confidence intervals. Compete against your fellow students for fame* and fortune^!
(* fame is subjective)
(^ there will be prizes for the winners)
Speaker: Ira Rothstein, Professor of Physics
Time: 5:30 on Wednesday, February 19, 2014
Location: DH 2315
Why are differential equations so ubiquitous? It seems that all physical systems are described by a set of differential equations. Perhaps we should stop and ask why? In this talk I will explain how a certain set of fundamental principle that apply to all physical systems automatically lead to differential equations (DE's) as equations of motion, as opposed to say integral equations. I will also discuss how the symmetries of physical systems, and their corresponding DE's, naturally lead to solutions via the use of group theory. Finally I will discuss how the principle of observer independence leads to the idea of differential geometry.