Archive

The resolution of Keller's conjecture

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.

Summer Experiences Panel

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.

No GBM on Wednesday, October 16th, 2019.

A Probabilistic Model for Gaps Between Primes

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.

Random Generation Methods for Binary Trees

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.

Impossible Roguelike: An Undecidability Result in Videogame Design

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.

DNA-driven Graph Theory

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.

Graph Splines and the Universal Difference Property

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.

Grad School Panel!

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!

Cryptographic Zero-Knowledge Proofs

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.

Course Selection

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.

Math Club Colloquium: Kristopher Lee

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.

Math Club Colloquium: David Offner

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.

Math Club Colloquium: Clive Newstead

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.

Math Club Colloquium: Mary Radcliffe

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.

The Random Initial Points Technique

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.

Making matrix factorization (more) useful

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.

Infinite Proofs can be Compact

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.

Traffic flow modeling: from game theory to differential equations

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.

Optimal Transport

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.

Undergraduate research in mathematical sciences

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.

No meeting on Wednesday, January 30.

Plank problem

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.

Games on Graphs

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.

Course Selection

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.

How to carve a pumpkin into... more pumpkins!

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.

Splitting loops and necklaces

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.

CMU-Pitt Trivia Night

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.

My functions are faster than yours

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.

A Brief Introduction to Problem Writing

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.

No meeting on Wednesday, September 26, 2018.

Internship Panel!

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!

Finding Meaning in Error Terms

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.

Senior Panel and Cake!

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!

Careers in Actuarial Science

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.

Coloring Linear Orders

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).

Course Selection

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.

A Case of Bad Handwriting

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.

Big Numbers

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.

The Fold and Cut Problem

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!

Where the Nonzero Things Are

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.

Taming Combinatorial Chaos through Imparital Game

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.

Modeling Cognition and Interdisciplinary Collaboration

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.

Game Night <3

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 Night

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!

Cycles

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.

Undergraduate Research Opportunities

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.

Monstruous Functions

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.

Have Yourself a Merry Little Christmas (Theorem)

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.

Constant Functions and Sobolev Spaces

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.

Mathematical Contest in Modeling Interest Meeting

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).

First General Body Meeting!

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!

Viscosity Solutions

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.

Star Numbers: from 17th-century oranges to delivery robots and beyond

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.

Counterintuitive Ideas in Analysis

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.

Fermi Questions

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?

Attenuated Tomography Old and New

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.

Some Applications of Differential Equations in the Social, Life, and Physical Sciences

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.

How to Multiply Big Numbers

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.

Triforce of Chaos Theory

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.

Sequences, Series, and Subterfuge

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.

Partial Differential Equations

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.

Geometry, Combinatorics, Patterns and Fun

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

Trigonometry Revisited or: If Fourier Had a Quantum Computer

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.

Thue Theorems and Avoidable Patterns

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

Infinite Dimension in Linear Algebra: A Case for Functional Analysis

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?

What is Structure?

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.

Probability and Intuition

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

Fine Structure in Shape-memory Alloys

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.

Variational Problems in Materials Science and Image Inpainting

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.

The Projective Heat Map

Speaker: Richard Schwartz, Chancellor`s Professor of Mathematics, Brown University

Time: 11:30 on Friday, Oct.16th, 2015

Location: WEH 8200

Abstract: Abstract and Slides

Meet-and-Greet with Paul Raff

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)

Triples

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.

Sticky Particles

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.

Unexpected distribution phenomenon resulting from Cantor series expansions

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.

Why the IRD cares about the Riemann Zeta Function and Number 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.

The Birch and Swinnerton-Dyer conjecture

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.

The Congruent Number Problem and Elliptic Curves

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.

Missing the Point

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.

Special Guest Speaker

Speaker: Noam Elkies, Professor of Mathematics, Harvard University

Time: 5:30 to 6:30 on Wednesday, December 3rd

Location: WEH 7500

TBA

The fundamental theorem of algebra

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.

You do not have to believe in transcendental numbers

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.

When IMO meets Research

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.

Assessing Artifacts: Using Calculus of Variations to Segment Damaged Images

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.

Chaos In Cellular Automata

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.

The Estimathon

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)

How Physics can help with the "Big Picture" in Math

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.