*Announcement - please share*
Mathematics in Science: Perspectives and Prospects
October 27–28, 2023
A showcase of mathematics in interaction with physics, computer science,
biology, and beyond.
This conference will be held in hybrid format, both in person and via Zoom
Webinar.
Registration is required.
In-person registration
<https://docs.google.com/forms/d/1xPRHQadCCEVInmVJ1yEhFMtCDA2upk7ca9E-yyFfkrE/viewform?edit_requested=true>
(link).
Zoom Webinar registration
<https://harvard.zoom.us/webinar/register/WN_tZoGPHKqSNio2w6a0r0i1A> (link).
Speakers
- Nima Arkani-Hamed <https://www.ias.edu/sns/arkani> (IAS)
- Constantinos Daskalakis <http://people.csail.mit.edu/costis/> (MIT)
- Alison Etheridge <https://www.stats.ox.ac.uk/people/alison-etheridge>
(Oxford)
- Mike Freedman <https://en.wikipedia.org/wiki/Michael_Freedman>
- Greg Moore <https://www.physics.rutgers.edu/~gmoore/>(Rutgers)
- Bernd Sturmfels
<https://www.mpg.de/11383459/mathematics-in-the-sciences-sturmfels>(MPI
Leipzig)
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
2:00–3:15 pm Greg Moore (Rutgers)
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.
3:15–3:45 pm *Break*
3:45–5:00 pm 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.
Saturday, October 28, 2023
9:00 am Breakfast
9:30–10:45 am Mike Freedman (Harvard CMSA)
Title: Some mathematical structures that may be useful for understanding
machine learning
Abstract: Vannila deep neural nets DNN repeatedly stretch and fold. They
are reminiscent of the logistic map and the Smale horseshoe. What kind of
dynamics is responsible for their expressivity and trainability. Is chaos
playing a role? Is the Kolmogorov Arnold representation theorem relevant?
Large language models are full of linear maps. Might we look for emergent
tensor structures in these highly trained maps in analogy with emergent
tensor structures at local minima of certain loss functions in high-energy
physics.
10:45–11:15 am Break
11:15 am–12:30 pm
via Zoom Nima Arkani-Hamed (IAS)
Title/Abstract TBA
12:30–2:00 pm Lunch break
2:00–3:15 pm Constantinos Daskalakis (MIT)
Title: How to train deep neural nets to think strategically
Abstract: Many outstanding challenges in Deep Learning lie at its interface
with Game Theory: from playing difficult games like Go to robustifying
classifiers against adversarial attacks, training deep generative models,
and training DNN-based models to interact with each other and with humans.
In these applications, the utilities that the agents aim to optimize are
non-concave in the parameters of the underlying DNNs; as a result, Nash
equilibria fail to exist, and standard equilibrium analysis is
inapplicable. So how can one train DNNs to be strategic? What is even the
goal of the training? We shed light on these challenges through a
combination of learning-theoretic, complexity-theoretic, game-theoretic and
topological techniques, presenting obstacles and opportunities for Deep
Learning and Game Theory going forward.
3:15–3:45 pm Break
3:45–5:00 pm 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.
Further details and a schedule
<https://live-hu-cmsa-222.pantheonsite.io/media/Schedule_mathinscience.pdf>are
available at:
*https://cmsa.fas.harvard.edu/event/mathematics-in-science/*
<https://cmsa.fas.harvard.edu/event/mathematics-in-science/>
[image: MathScience2023Poster_8.5x11.png]
--
Maureen Armstrong | *Publications Coordinator*
Center of Mathematical Sciences and Applications
Harvard University
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