PIMS lectures
Title: Machine assisted proofs
Speaker: Terence Tao, UCLA
Date and time:
10 Sep 2024,
2:00pm -
3:00pm
Location: Online. Registration required
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The Colloquium Series was inaugurated in 2021 for distinguished speakers to give talks across the full PIMS network with one talk per month during the main academic term.
Register here.
Abstract: For centuries, mathematicians have relied on computers to perform calculations, to suggest conjectures, and as components of mathematical proofs. In the light of more modern tools such as interactive theorem provers, machine learning algorithms, and generative AI, we are beginning to see machines used in more creative and substantive ways in our work. In this talk we survey some historical and recent developments, and speculate on the future roles of machine assistance in mathematics.
Title: Discrete Gaussian Free Field and Invariant Measures for the Non-Linear Schrödinger Equation
Speaker: Kesav Krishnan, University of Victoria
Date and time:
20 Mar 2024,
9:30am -
10:30am
Location: via Zoom registration required
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For more information and registration: https://www.pims.math.ca/seminars/PIMSPDF.
ABSTRACT:
In this talk, I will describe how certain non-linear
exponential tilts of the Discrete Gaussian Free Field yield
invariant measures for a discretized PDE, the focusing Non
Linear Schrödinger equation. I will briefly talk about how this
tilted measure relates to self-intersections of the random
walk on $\mathbb{Z}^{d}$. I will then describe joint work
with Partha Dey and Kay Kirkpatrick on how this measure
undergoes a phase transition in the thermodynamic limit
with general $d\geq 3$ and non-linearity $p$. I will conclude
with some new results with Gourab Ray, on the weak
convergence of the random field sampled with respect to
this measure to the massive discrete Gaussian Free Field.
SPEAKER BIO:
Kesav is a PIMS postdoctoral fellow at the University
of Victoria who works with Gourab Ray. Kesav’s
academic trajectory began as an undergraduate
student in physics at the University of Delhi. After
realizing that mathematical methods (specifically
probability) excited him more, Kesav switched
track and completed his masters in mathematics
at the Indian Statistical Institute, Bangalore.
As a PhD student at the University of Illinois,
Urbana-Champaign, Kesav focused on problems
in probability that have origins in statistical and
mathematical physics. He continues to work in
this field, specifically on phase transitions in
lattice field theories and disordered models in
statistical mechanics. He is thrilled to have gotten
the opportunity to spend two years in the Pacific
Northwest and explore its spectacular natural
beauty.
Download poster (PDF).