01/23/2026 – Chase Bender: Rational Surfaces: Example One in Birational Geometry
Abstract: Birational geometry is a subfield of algebraic geometry which has flourished in recent history—especially in dimensions 3 and above—due to the foundation laid by Grothendieck’s scheme theory. Much of this progress is mo- tivated by the more classically understood theory of complex projective surfaces, and in the particular case of rational surfaces many of the typical actors of bira- tional geometry can be grounded via analogy to real geometry. In this talk I will give “low tech” definitions of rational surfaces and the structural components of birational geometry in this setting, as well as state theorems in this setting which are prototypical of the more general field of study.
01/30/2026 – Soham Jana: Theoretical limits for speckle noise modeling in high-dimensional image sensing
Abstract: Recent advances in speckle noise modeling via multiplicative errors have raised many critical questions. Deep learning-based methods have been proven fruitful for analyzing sensor data and reconstructing images when the signal resides in a low-dimensional space. However, the existing guarantees for such methods are far from being optimal. In addition, the problem becomes challenging when the number of sensors is very small compared to the image dimension, and it is often necessary to take multiple images of the scene to enable consistent reconstruction. Our recent work establishes estimation thresholds (by obtaining minimax lower bounds and constructing algorithms with matching upper bounds) for such problems when the signal can arise from either low- or high-dimensional regimes. Real and simulated data analyses support the efficiency of our estimation techniques.
02/06/2026 – Simons Fellowship Panel
Abstract: Discussion about the Simons Dissertation Fellowship with previous applicants and awardee.
02/13/2026 – Mattie Ji: Teaching Algebraic Topology Using Electrical Circuits
Abstract: In this talk, I will describe a perspective, originally due to Weyl in 1923, that fundamental concepts in electrical circuits can be naturally interpreted as statements about homology and cohomology of graphs. Thus, one can motivate and introduce the theory of (co)homologies using electrical circuits, which is the approach this talk would take. No prior knowledge of electrical circuits or (co)homologies are necessary. If time permits, I may try to sketch some work I have on what are called “brave new / homotopical electrical circuits”, which I plan to post on April 1st, 2026.
02/20/2026 – Katie Ellman-Aspnes: Classification Theory and the Map of the Universe
Abstract: Model theory enables us to analyze the complexity of various mathematical objects that are structurally very different, such as a graph with a group or a field with a topological space. In this talk we’ll discuss what it means for a mathematical object to be classifiable and some indicators of complexity that show when an object is not classifiable. We’ll also take a look at the model-theoretic “map of the universe,” which is a means of visually organizing various types of mathematical objects according to model-theoretic degrees of complexity.
02/27/2026 – Cory Gillette: A Friendly Introduction to Monads
Abstract: Monads are one way of making formal sense of what we mean when we speak about sets “equipped with some structure”. We will try to give enough examples to convince you that these occur frequently in nature. We will also discuss some theorems and applications. We will not assume familiarity with category theory.
03/06/2026 – Joshua Lehman: The Degree-Genus Formula
Abstract: Algebraic curves in the complex projective plane are, topologically, two dimensional surfaces. I’ll give three different ways of computing their genus and draw pictures of (nice) curves (don’t worry, drawing a squiggly line doesn’t count!).
03/13/2026 – SPRING BREAK: NO TALK
03/20/2026 – Academic jobs panel
Abstract: We are very lucky to have Annie Holden, Jui-Yun Hung, Katherine Novey (all current ND grad students), and Lorenzo Riva (a previous ND grad student) who will talk to us about their experiences of academic job applications and try to answer any questions we may have.
03/27/2026 – Chen-Kuan Lee: Riemannian Holonomy and Berger’s List
Abstract: Riemannian geometry is a branch of differential geometry that studies manifolds equipped with a Riemannian metric, which provides a way to measure distances and angles. In this talk, we will introduce the concept of holonomy groups, with a focus on Riemannian holonomy. We will then discuss how holonomy interacts with the topology of manifolds by highlighting Berger’s classification of possible Riemannian holonomy groups.
04/03/2026 – EASTER BREAK: NO TALK
04/10/2026 – Tan Özalp: A Hat Problem
Abstract: We describe a game of prisoners and hats and construct a non-measurable function.
04/17/2026 – NO TALK
04/24/2026 – Jenny Xu: Compact Right Topological Semigroups and their Idempotents
Abstract: I will talk about compact right topological semigroups, their idempotents, and maybe Hindman’s theorem.
05/01/2025 – Luis Atzin Franco-Reyna: (Not WIRED) 4 Levels of Calculus of Variations in Geometry
Abstract: One of the most elegant ideas in math is the idea of optimization of a function. The tools of carrying out this procedure are manifold (pun intended), one of which is the calculus of variation. Mimicking the famous WIRED 5 level series, I will attempt to explain this idea in 4 levels that (hopefully) is easily understandable.