New Technologies in Mathematics Seminar Speaker: Tatsunori Hashimoto, Stanford Title: New directions in synthetic data Abstract: Synthetic data has been an effective, if boring set of techniques: prompt some language model to restructure your corpus to match some downstream task, with occasionally some distillation. In this talk, we will take a more expansive view of […]
Freedman Seminar Speaker: Mike Freedman, Harvard CMSA Title: Compression Is All You Need: Modeling Mathematics Abstract: The talk will exposit a recent eponymous arXiv posting with coauthors Vitaly Aksenov, Eve Bodnia, and Mike Mulligan. The approach is to think like a physicist and model a seemingly complex bit of reality: mathematics, by a simple toy […]
Freedman Seminar Speaker: Robert Gompf, UT Austin Title: Exotic R^4's are unclassifiable Abstract: We will use descriptive set theory to show that there is a precise sense in which exotic R^4's are unclassifiable. For other open manifolds, we can reach a much higher level of unclassifiability. This is work in progress with Aristotelis Panagiotopoulos.
New Technologies in Mathematics Seminar Speaker: Emmanuel Abbé, EPFL, Institute of Mathematics and School of Computer and Communication Sciences & Apple Title: Dynamic reasoning Abstract: In the current AI landscape, reasoning is frequently equated with the generation of intermediate "thinking traces". However, these traces are merely a mechanism, not the ultimate objective. Relying solely on the presence of […]
New Technologies in Mathematics Seminar Speaker: Yiannis Vlassopoulos, Athena Research Center Title: ReLU and Softplus neural nets as zero-sum, turn-based, stopping games Abstract: Neural networks are for the most part treated as black boxes. In an effort to begin elucidating the mathematical structure they encode, we will explain how ReLU neural nets can be interpreted as […]
New Technologies in Mathematics Seminar Speaker: Adam Zsolt Wagner, Google DeepMind Title: Machine learning tools for mathematical discovery Abstract: I will discuss various ML tools we can use today to try to find interesting constructions to various mathematical problems. I will briefly mention simple reinforcement learning setups and PatternBoost, but the talk will mainly focus […]
Differential Geometry and Physics Seminar Speaker: Andrés Franco Valiente, UC Berkeley Title: Tropical-Topological (Tropological) Sigma Models Abstract: Tropical geometry provides a powerful bridge between complex and combinatorial worlds, allowing certain curve-counting invariants to be computed in a piecewise-linear “tropical” limit. Building on Mikhalkin’s insight that Gromov–Witten invariants can be recovered from tropical curves, this talk revisits Mikhalkin's […]
Freedman Seminar Speaker: Michael Freedman, Harvard CMSA Title: Sullivan’s work on Lipschitz structures Part II (but self-contained) Speaker: Bowen Yang, CMSA Title: Deligne and Sullivan's work on complex bundles with discrete structure group
New Technologies in Mathematics Seminar Speaker: María Inés de Frutos Fernández, Mathematical Institute, University of Bonn Title: The Carleson project: A collaborative formalization Abstract: A well-known result in Fourier analysis establishes that the partial Fourier sums of a smooth periodic function $f$ converge uniformly to $f$, but the situation is a lot more subtle for […]
Freedman Seminar Speaker: Michael Freedman, Harvard CMSA Title: Sullivan's work on Lipschitz structures Abstract: I'll begin with an elementary, but now little known, piece of PL topology: engulfing. John Stalling used it to give an alternative proof of the high dimensional Poincare conjecture. Then I'll explain Dennis Sullivan's enhancement of Kirby's torus trick (which relies […]
Algebra Seminar Speaker: Linquan Ma (Purdue University) Title: Lech's inequality and stability of local rings Abstract: We explore Lech's inequality relating the colength and multiplicity of m-primary ideals in a Noetherian local ring (R,m). We introduce a natural invariant that measures the sharpness of Lech's inequality and show its connections with singularities of asymptotically semistable varieties […]
Quantum Field Theory and Physical Mathematics Seminar Speaker: Kevin Costello (Perimeter Institute) Title: Non-perturbative aspects of self-dual gauge theory Abstract: Self-dual gauge theory is conformal in perturbation theory, but has a non-trivial beta-function when instanton effects are included. I will give two computations of this beta-function, one based on the Grothendieck-Riemann-Roch formula and one using holography […]