Math Club Seminars

Krieger 413

Johns Hopkins University

Tuesdays 6:30 - 7:30 pm

Academic Year 2024 - 2025

Go here for more information.

Dinner will be served at the meetings.

Spring 2025 Schedule

02/04: Daniel Carranza

Title: An invitation to discrete homotopy theory

Abstract: Discrete homotopy theory, introduced around 20 years ago by H. Barcelo and collaborators building on the work of R. Atkin from the mid-seventies, is a homotopy theory of (simple) graphs. As such, it applies techniques previously employed in the "continuous" context to study discrete objects. It has found applications both within and outside mathematics, including: matroid theory, hyperplane arrangements, topological data analysis, and more. This talk will be an introduction to discrete homotopy theory, including recent applications of abstract homotopy theory to resolve conjectures in the field (arXiv:2202.03516). No prior knowledge of either homotopy theory or combinatorics will be assumed.

⭐02/14 (4pm)⭐: Ko Ohm

Title: Covering Lemmas in Analysis and Geometry

Abstract: Covering lemmas are fundamental tools in mathematical analysis, with deep connections to the geometry of Euclidean spaces. In this talk, we will explore key classical results, such as the Vitali and Besicovitch covering theorems, and discuss their significance in measure theory, differentiation, and geometric analysis.

02/18: Tim Campion

Title: A survey of enriched categories

Abstract: We'll recall some rudiments of the notion of a category, including some examples such as the category Set of sets and functions, the category Vect of vector spaces and linear maps, the category Top of topological spaces and continuous maps, etc. We'll then delve into the notion of an enriched category, where the morphisms between two objects form some mathematical entity other than a set. As a surprising example (first observed by Lawvere), a metric space may be viewed as a category enriched in the category of real numbers. We’ll explore how various categorical ideas can be transported between different enriched settings.

⭐02/21 (6pm, Krieger 413)⭐: Alex Shumakovitch

Title: On applications of Topology

Abstract: I will explain how knowledge of Topology helped with winning the Nobel Prize in Physics 2016. No familiarity with advanced math beyond Calculus will be assumed from the audience.

02/25: Alvaro Belmonte

Title: Generalized Bondage Number: The k -synchronous bondage number of a Graph

Abstract: In this talk I will introduce the notions of domination, domination number, and bondage number on a graph. We will generalize the notion to k-synchronous bondage number, mainly the case when k = 2. We will present k-synchronous bondage number for several graph classes.

⭐02/27 (5pm, Krieger 411)⭐: Julianne Rainbolt

Title: Wait! That Cannot Be Right

Abstract: In this talk proofs will be presented that contain an incorrect step or include an incorrect assumption. This will lead us to prove concepts that are clearly false. This incorrect step or assumption will not be obvious, in fact the proofs will be presented in a way to try to hide the errors. Come see if you can discover the mistake in each argument!

03/04: Graduate School Open House (Jacob Bernstein, Caterina Katia Consani, Nitu Kitchloo)

Title: Panel about Graduate Schools

Abstract: This event will feature a panel of faculty from our math department to provide support for students seeking to learn more about the process of applying to graduate school in mathematics. It will help students choose schools based on interests and gain unique insights into what the whole process entails.

03/11: Rok Gregoric

Title: Stone duality from a few points of view

Abstract: The motto "geometry/topology is just algebra, but in reverse" can be made precise in various contexts. One of its simplest instances is Stone duality.

Stone duality is a particularly compelling result since it connects objects of many different sorts! On one side are Boolean algebras, important in logic and computer science, as well as abstract algebra in general and ring theory in particular. On the other side is a certain seemingly-pathological topological class of spaces - including as example the famous Cantor set - and equivalent to pro-finite sets, structures which in various guises show up (for instance via p-adic numbers, and via absolute Galois groups) in number theory.

In this talk, we will explain the two sides of Stone duality, how they are connected, and some (but by no means all!) ways that Stone duality can be extended, expanding the scope of the motto cited above.

We will not aim for a very high level of technical precision, so while familiarity with basic point-set topology, abstract algebra, and the language of category theory might come in handy to better appreciate some finer points, it should not be a necessary prerequisite to get something out of the talk.

⭐03/14 (2 - 3:30pm, Krieger 413)⭐: Pi Day

Title: Join us for plenty of pizza and a great selection of pies!

Abstract: RSVP with the Department of Mathematics front desk, i.e., Jordan White, by filling out the Pi Day Invitation form.

03/18: Spring Break

03/25: Nathan Breslow

Title: The Ghost in The Machine Is Just Linear Algebra

Abstract: The mathematics behind cutting edge AI (ChatGPT, Claude, Gemini, etc.) are surprisingly simple - requiring no more than elementary linear algebra and multivariable calculus applied at scale. This talk will explore how modern AI ingeniously reframes all of natural language processing as a f: [ℕ] → ℕ function, learns this function at scale, and what the internals of this function consist of (self-attention, feed forward networks, etc.) Background required is knowledge of matrices and calculus. Basic understanding of optimization techniques like gradient descent is preferred.

04/01: Tyler Wunder and Jorge Gonzalez

Title: Surfaces and Differential Geometry

Abstract: Informally, differential geometry is using calculus to study smooth objects. More formally, it is the study of smooth objects that locally look like R^n. Classically, differential geometry is the study of smooth curves (informally bent lines) and surfaces (informally bent paper) inside of three-dimensional space.

In this talk, we will define and discuss the basic theory of surfaces. We will explore the ideas around tangent spaces, the Gauss map, curvature, and integration on surfaces. We will then finish with a proof of one of the most interesting and important theorems in classical differential geometry: Alexandrov’s Theorem, which states that any compact, connected surface with constant mean curvature is a sphere.

⭐04/05 (4:30 - 6:00 pm, Bloomberg 462)⭐: Math Club Mixer with SPS

Title: Math Club Mixer with the Society of Physics Students JHU

Abstract: We will be having a a mixer with the undergrad physics club SPS on Friday in Bloomberg 462 at 430pm. We will have jeopardy, lots of nice free food, an integration bee, and other fun activities planned! Come by for a fun time!

04/08: Nicholas Rugo and Fabian Espinoza de Osambela

Title: An Introduction to the Koszul Complex

Abstract: In this talk we will explore the motivation, definition, and usage of the Koszul complex. We will specifically pay attention to examples of Koszul complexes in geometry, representation theory, and analysis. Ideally the audience knows some linear algebra and abstract algebra.

04/15: James Guo

Title: Hausdorff Measure and Fractal Geometry

Abstract: In this talk, we will explore the motivations and step-by-step construction of Hausdorff measure and Hausdorff dimension for the sets that would have been interpreted as a null set in the Lebesgue measure. Examples with some fractal geometry will be discussed. Audiences are expected to know basic calculus and middle school geometry, but it would be helpful if the audiences are exposed to basic measure theory ideas.

04/22: Nooria Ahmed

Title: Derivatives and Tangents In Increasing Abstraction

Abstract: Derivatives? Heck yeah. Approximating more complex functions locally via linear approximations? Radical. Understanding tangent spaces on manifolds? Tubular. But what if you like algebra and category theory like I do? In both cases, you can give objects of interest an underlying "geometry," one that can be studied using abstracted notions of derivatives, (co)tangent bundles and linearity.

In this talk we will construct the algebraic and categorical generalization of derivatives, the cotangent complex and one-forms via the language of Kahler differentials and square-zero extensions. In doing so, we will hopefully be able to introduce some basic ideas from deformation theory. Depending on time, we may also be able to discuss applications to Kodaira-Spencer theory.

04/29: Wrap-Up Meeting

Title: Wrap-Up Social

Abstract: We will discuss the semester's successes and failures. We will also discuss plans and improvements going forward!

04/30 (Wednesday, 3:00-5:00 pm, Krieger 413): Awards Day 2025

Title: Awards Day 2025

Abstract: This event features catering. Please respond to the Front Office if you plan to attend.

Fall 2024 Schedule

09/03: Welcome back socialization/organization

09/10: Talk Workshop 1: choosing a topic

09/17: Talk Workshop 2: writing an outline

09/24: Yueqiao Wu

10/01: Talk Workshop 3: writing an abstract, practice