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 […]
General Relativity Seminar Speaker: Sifan Yu, National University of Singapore Title: Low-regularity Local Well-posedness of the Elastic Wave System Abstract: In this talk, I will present a recent work on the elastic wave system in three spatial dimensions. For admissible harmonic elastic materials, we prove a low-regularity local well-posedness result for the corresponding elastic wave equations. For such materials, we can split the […]
https://youtu.be/TFBzP78Jp6A New Technologies in Mathematics Seminar Speaker: Thomas Hubert (Google DeepMind) Title: AlphaProof: when reinforcement learning meets formal mathematics Abstract: Galileo, the renowned Italian astronomer, physicist, and mathematician, famously described mathematics as the language of the universe. Progress since only confirmed his intuition as the world we live in can be described with extreme precision […]
Mathematical Physics and Algebraic Geometry Seminar *via Zoom only* Speaker: Tianqing Zhu (Tsinghua University) Title: From quantum difference equations to Maulik-Okounkov quantum affine algebra Abstract: Capping operator is one the core subject in the K-theoretic quasimap counting to quiver varieties. It has been shown by Okounkov and Smirnov that it satisfies a system of q-difference […]
https://youtu.be/2Aak8YqVsLw General Relativity Seminar Speaker: Elliot Marshal, School of Mathematics at Monash University Title: Unstable Fluids in Expanding Cosmologies Abstract: The FLRW solution is the simplest cosmological model in general relativity, describing a fluid-filled, spatially homogeneous universe. While there is extensive literature in the physics community on cosmological models with a linear equation of state , […]