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 […]
https://youtu.be/0FCgpyCfb4o New Technologies in Mathematics Seminar Speaker: Michael Borinsky, Perimeter Institute Title: Tropicalized quantum field theory Abstract: Quantum field theory (QFT) is one of the most accurate methods for making phenomenological predictions in physics, but it has a significant drawback: obtaining concrete predictions from it is computationally very demanding. The standard perturbative approach expands an […]
Mathematical Physics and Algebraic Geometry Seminar Speaker: Joaquin Liniado, Instituto de Física La Plata Title: Higher Gauge Theory and Integrability Abstract: Integrable field theories are remarkable for possessing an infinite number of conserved quantities, which often allow for their exact solvability. In two dimensions, this structure is elegantly captured by the existence of a Lax […]
Mathematical Physics and Algebraic Geometry Seminar Speaker: Zhenping Gui, Shanghai Institute for Mathematics and Interdisciplinary Sciences Title: Residues and homotopy Lie algebras Abstract: I will introduce the notion of a chiral operad for any compact Riemann surface. This operad consists of compositions of residue operations, which give rise to the Chevalley-Cousin complex and lead to the […]
Freedman CMSA Seminar Speaker: Slava Dzhenzher, MIPT Title: Adversarial KA Abstract: Regarding the representation theorem of Kolmogorov and Arnold (KA) as an algorithm for representing or «expressing» functions, we test its robustness by analyzing its ability to withstand adversarial attacks. We find KA to be robust to countable collections of continuous adversaries, but unearth a […]
Mathematical Physics and Algebraic Geometry Seminar Speaker: Ki Fung Chan (Chinese University of Hong Kong) Title: 3d Mirror Symmetry is 2d Mirror Symmetry Abstract: We introduce an approach to studying 3d mirror symmetry via 2d mirror symmetry. The main observations are: (1) 3d brane transforms are given by SYZ-type transforms; (2) the exchange of symplectic and complex […]