Colloquia & Seminars

Title: The Geography of Symplectic 4-Manifolds

Colloquium Speaker: Anar Akhmedov, University of Minnesota Title: The Geography of Symplectic 4-Manifolds Abstract: The symplectic geography problem, originally posed by J. McCarthy-J. Wolfson and R. Gompf, asks which ordered pairs of nonnegative integers are realized as (\chi(X),c_1^2(X)) for a symplectic 4-manifold X, where \chi(X)=(e(X)+\sigma(X))/4. In this talk, we will address the geography of simply connected spin and nonspin symplectic 4-manifolds with small Euler characteristic, with nonnegative signature, or near the Bogomolov-Miyaoka-Yau line c_1^2(X)=9\chi_h(X). We will also discuss recent developments, including joint work with Sai-Kee Yeung on symplectic fake quadrics and related questions motivated by fake projective planes and Cartwright-Steger surfaces.   To subscribe or unsubscribe to the colloquium mailing list, please visit this link.

Title: A Rigorous Construction of the Free Quantum Field

Joint Math/CMSA Geometry and Quantum Theory Seminar Speaker: Kason Kunkelmann, Harvard Title: A Rigorous Construction of the Free Quantum Field Abstract: In this talk we will build on last week’s discrete intuition and rigorously construct our first continuum quantum field theory: the free field. Following Chapter three of Chatterjee’s notes, we will realize it as a Gaussian random field in Euclidean spacetime, prove that it has the Markov property in time, and then use the procedure outlined in previous lectures to get its Hilbert space and Hamiltonian.

Title: CMSA Q&A Seminar

CMSA Q&A Seminar Speaker: tba    

Title: The IEANTN Project: Automation and Mathematical Understanding

New Technologies in Mathematics Seminar Speaker: Xinjie He, UCLA Title: The IEANTN Project: Automation and Mathematical Understanding Abstract: Explicit analytic number theory combines conceptual arguments with extensive bookkeeping and numerical computation, often drawing on long chains of results across many papers. The Integrated Explicit Analytic Number Theory Network (IEANTN) aims to organize this literature into a living network whose dependencies and supporting evidence are explicit. In this talk, I will discuss how we redesigned IEANTN from its 1.0 version, which put everything in a single Lean repository that was hard to maintain and rebuild as auto-formalization produces increasingly large proofs, to its current 2.0 version, which solves this problem by separating readable mathematical statements from verified proofs and...

Title: A ‘Deep Blue-Kasparov moment for mathematics’

AI for the Working Mathematician Speaker: Tristan Buckmaster, NYU Title: A 'Deep Blue-Kasparov moment for mathematics' Abstract: In this talk I will describe recent work with Levent Alpöge proving the blow-up for smooth solutions to the incompressible Euler equations and the broader implications that such results have of the study of mathematics.

Title: Geometry and Mathematical Physics Seminar

Geometry and Mathematical Physics Seminar Speaker: Elliott Gesteau (MIT & CMSA)  

Title: Poincaré Duality in Quantum Error-Correcting Codes

Member Seminar Speaker: Bowen Yang Title: Poincaré Duality in Quantum Error-Correcting Codes Abstract: Quantum information is fragile, and one of the main tools for protecting it is a family of error-correcting codes called stabilizer codes. These codes have a second life as exactly solvable models of quantum matter: the code space is the vacuum state and the "syndromes" behave like excitations that can move freely, get stuck in place, or wind around one another. I will show how a little homological algebra packages these excitations into clean mathematical objects, which we call charge modules. Moreover, there are natural pairing between different charge modules of complementary degrees sometimes called "braiding". They actually came from the Poincare duality of the...

Title: Extreme Diffusion

Colloquium Speaker: Ivan Corwin (Columbia University) Title: Extreme Diffusion Abstract: Two hundred years ago, Robert Brown observed the statistics of the motion of grains of pollen in water. It took almost one hundred years for Einstein and others to develop an effective theory describing this motion as that of a random walker. In this talk, I will challenge a key implication of this well established theory. When studying systems with very large numbers of particles diffusing together, I will argue that the Einstein random walk theory breaks down when it comes to predicting the statistical behavior of extreme particles—those that move the fastest and furthest in the system. In its place, I will describe a new theory of extreme diffusion which captures...

Title: Geometry and Quantum Theory Seminar

Joint Math/CMSA Geometry and Quantum Theory Seminar Speaker: Tobias Schmidt  

Title: New Technologies in Mathematics Seminar

New Technologies in Mathematics Seminar Speaker: Yasaman Bahri (Google DeepMind)

Title: AI for the Working Mathematician

AI for the Working Mathematician Speaker: Andrew Sutherland, MIT Title: TBA

Title: Geometry and Mathematical Physics Seminar

Geometry and Mathematical Physics Seminar Speaker: Ron Donagi, University of Pennsylvania

Title: Member Seminar

Member Seminar  

Title: Colloquium

Colloquium Speaker: Lukas Müller (LMU Munich)         To subscribe or unsubscribe to the colloquium mailing list, please visit this link.

Title: Geometry and Quantum Theory Seminar

Joint Math/CMSA Geometry and Quantum Theory Seminar