A showcase of mathematics in interaction with physics, computer science, biology, and beyond.

October 27–28, 2023

Location: Harvard University Science Center Hall D & via Zoom.

Directions and Recommended Lodging

Format: This conference will be held in hybrid format, both in person and via Zoom Webinar.

Registration is required.

In-person registration (link).

Zoom Webinar registration (link).

Organizers

• Michael R. Douglas (Harvard CMSA)
• Dan Freed (Harvard Math & CMSA)
• Mike Hopkins (Harvard Math)
• Cumrun Vafa (Harvard Physics)
• Horng-Tzer Yau (Harvard Math)

Schedule

Friday, October 27, 2023

2:00 pm–5:00 pm

Saturday, October 28, 2023

9:00 am–5:00 pm

Limited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register above and send an email to mathsci2023@cmsa.fas.harvard.edu no later than September 25, 2023.

Please include your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc, please include a copy of your CV.

Titles and Abstracts 

(further details TBA)

Speaker: Alison Etheridge (Oxford)

Title: Modelling hybrid zones

Abstract: Mathematical models play a fundamental role in theoretical population genetics and, in turn, population genetics provides a wealth of mathematical challenges. In this lecture we investigate the interplay between a particular (ubiquitous) form of natural selection, spatial structure, and, if time permits, so-called genetic drift. A simple mathematical caricature will uncover the importance of the shape of the domain inhabited by a species for the effectiveness of natural selection.

Speaker: Gregory Moore

Title: Remarks on Physical Mathematics

Abstract: I will describe some examples of the vigorous modern dialogue between mathematics and theoretical physics (especially high energy and condensed matter physics). I will begin by recalling Stokes’ phenomenon and explain how it is related to some notable developments in quantum field theory from the past 30 years. Time permitting I might also say something about the dialogue between mathematicians working on the differential topology of four-manifolds and physicists working on supersymmetric quantum field theories. But I haven’t finished writing the talk yet, so I don’t know how it will end any more than you do.

Speaker: Bernd Sturmfels (MPI Leipzig)

Title: Algebraic Varieties in Quantum Chemistry

Abstract: We discuss the algebraic geometry behind coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schroedinger equation are approximated by a hierarchy of polynomial systems at various levels of truncation. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Pluecker embedding. We explain how to derive Hamiltonians, we offer a detailed study of truncation varieties and their CC degrees, and we present the state of the art in solving the CC equations. This is joint work with Fabian Faulstich and Svala Sverrisdóttir.