Colloquia & Seminars

Title: A Rigorous Construction of the Free Quantum Field

Joint Math/CMSA Geometry and Quantum Theory Seminar Speaker: Kason Kunkelmann 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: What is a self-concordant barrier function?, and what is an accelerated first-order algorithm?  (ICM Series: On the work of Yurii Nesterov)

CMSA Q&A Seminar Speaker: Robert M. Freund, MIT Title: What is a self-concordant barrier function?, and what is an accelerated first-order algorithm?  (ICM Series: On the work of Yurii Nesterov) Abstract: The two most impactful contributions of Nesterov on both theory and computation in optimization are (i) self-concordant barriers for interior-point methods in convex optimization, and (ii) accelerated first-order methods for convex optimization. My own research in continuous optimization – and indeed my perspective on the field of mathematical optimization -- has been profoundly impacted by Nesterov. In this talk I aim to explain these two contributions – self-concordant barriers and accelerated first-order methods – and how they have fundamentally improved optimization both computationally and theoretically.      

Title: CMSA Q&A Seminar

CMSA Q&A Seminar Speaker: tba    

Title: Local learning needs dendrites

New Technologies in Mathematics Seminar Speaker: Riccardo Zecchina (Bocconi University) Title: Local learning needs dendrites Abstract: I will present a learning scheme for recurrent networks in which nonlinear dendrites enable learning by generating and stabilizing task-relevant attractors within a representation manifold. The scheme is local in space and time and matches the performance of backpropagation through time on the same architecture, while following a fundamentally different trajectory in weight space. Statistical physics reveals how dendritic gating and the geometry of the representation manifold support this alternative route to learning.

Title: Geometry and Mathematical Physics Seminar

Geometry and Mathematical Physics Seminar  

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: Geometry and Quantum Theory Seminar

Joint Math/CMSA Geometry and Quantum Theory Seminar  

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: AI for the Working Mathematician

AI for the Working Mathematician Speaker: Tristan Buckmaster, NYU Title: TBA

Title: Geometry and Mathematical Physics Seminar

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

Title: Member Seminar

Member Seminar Speaker: Houcine Ben Dali  

Title: Colloquium

Colloquium Speaker: Ivan Corwin (Columbia University)         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 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