Upcoming talk:
CMSA/Tsinghua Math-Science Literature Lecture: Bjorn Poonen, MIT
Time：10:00 pm, Nov. 21, 2024 (Beijing Time)
Speaker: Bjorn Poonen, MIT
Title: Ranks of elliptic curves
Abstract: Elliptic curves are simplest varieties whose rational points are not fully understood, and they are the simplest projective varieties with a nontrivial group structure. In 1922 Mordell proved that the group of rational points on an elliptic curve is finitely generated. We will survey what is known and what is believed about this group.
https://harvard.zoom.us/webinar/register/WN_7stTVO1cRPi8hxjt0KYm9Q
Past talks:
Math Science Lectures in Honor of Raoul Bott
Andrew Neitzke, Yale University
Harvard University Science Center Hall D & via Zoom webinar
October 16 & 17, 2024 ET
4:00 – 5:30 pm ET
Register for in-person attendance
Zoom Webinar registration
Wednesday, Oct. 16, 2024 ET
Title: Abelianization in analysis of ODEs
Abstract: I will describe the exact WKB method for asymptotic analysis of families of ODEs in one variable, and its interpretation as a kind of abelianization procedure, which replaces GL(N)-connections over a Riemann surface by GL(1)-connections over an N-fold branched cover. This abelianization procedure connects exact WKB to various subjects in geometry (cluster algebras, moduli of Higgs bundles, enumerative geometry). One application is a conjectural description of Hitchin’s hyperkahler metric on the moduli of Higgs bundles; I will review some recent progress on these conjectures.
Thursday, Oct. 17, 2024 ET
Title: Abelianization in quantum topology
Abstract: I will describe new applications of abelianization to various related subjects: perturbative Chern-Simons invariants, skein algebras, and conformal blocks. The aim is to explain how abelianization gives a unifying perspective on constructions familiar in each of these subjects (e.g. dilogarithmic formulas for Chern-Simons invariants, vertex models for computing quantum invariants of links, and iterated-fusion constructions of conformal blocks for the Virasoro algebra), and also suggests various extensions, which are just beginning to be explored.
https://cmsa.fas.harvard.edu/event/mathscibott_1024
Bott Lecture_Neitzke.png
CMSA/Tsinghua Math-Science Literature Lecture
Wednesday, September 18, 2024
9:00 – 10:30 am ET
via Zoom Webinar
Register for Zoom Webinar
Speaker: Marc Lackenby, University of Oxford
Title: The complexity of knots
Abstract: In his final paper in 1954, Alan Turing wrote `No systematic method is yet known by which one can tell whether two knots are the same.’ Within the next 20 years, Wolfgang Haken and Geoffrey Hemion had discovered such a method. However, the computational complexity of this problem remains unknown. In my talk, I will give a survey on this area, that draws on the work of many low-dimensional topologists and geometers. Unfortunately, the current upper bounds on the computational complexity of the knot equivalence problem remain quite poor. However, there are some recent results indicating that, perhaps, knots are more tractable than they first seem. Specifically, I will explain a theorem that provides, for each knot type K, a polynomial p_K with the property that any two diagrams of K with n_1 and n_2 crossings differ by at most p_K(n_1) + p_K(n_2) Reidemeister moves.
Prof. Amie Wilkinson will present a lecture in the CMSA/Tsinghua Math-Science Literature Lecture Series.
Date: Wednesday, February 7, 2024
Time: 9:00–10:30 am ET
Location: Via Zoom Webinar
Registration is required.
Details: https://cmsa.fas.harvard.edu/event/mathscilit2024_aw/
Title: Large cardinals and small sets: The AD+ Duality Program
Speaker: Hugh Woodin,Professor of Mathematics and Philosophy @ Harvard University
Date: Wednesday, November 9, 2022
Time: 9:30 – 11:00 am ET (22:30-24:00,Beijing Time）
Location: Via Zoom Webinar and Room G10, CMSA, 20 Garden Street, Cambridge MA 02138
Register here to attend virtually: https://harvard.zoom.us/webinar/register/WN_m6xxiwmuTGGGPd2IVaUYTQ
Abstract:
The determinacy axiom, AD, was introduced by Mycielski and Steinhaus over 60 years ago as an alternative to the Axiom of Choice for the study of arbitrary sets of real numbers. The modern view is that determinacy axioms concern generalizations of the borel sets, and deep connections with large cardinal axioms have emerged.
The study of determinacy axioms has led to a specific technical refinement of AD, this is the axiom AD+. The further connections with large axioms have in turn implicitly led to a duality program, this is the AD+ Duality Program.
The main open problems here are intertwined with those of the Inner Model Program, which is the central program in the study of large cardinal axioms.
This has now all been distilled into a series of specific conjectures.
CMSATsinghua Math-Science Literature Lecture-Mathlit_WOODIN.pdf
