YouTube channel

Schedule of talks:

Abstracts

(L. Levine): Aligning AI with human values is a pressing unsolved problem. How can mathematicians contribute to solving it? We can start by clarifying the terms: What are values? What does it mean to "align" an AI to a given set of values? And how would one verify that a given AI is aligned? These hard questions, plus the annoying little issue of whose values to prioritize, led researchers at leading AI labs to aim instead for "intent alignment": AI that (wants to) do what its developers intend. Can intent alignment deliver a good future, where humans thrive alongside AI that's much smarter than us? I'll argue that intent alignment might be extremely hard to achieve, and that it's neither necessary nor sufficient for a good future. Our best shot at a good future is to not build superhuman AI. Not building superhuman AI is a coordination problem: it would require international treaties, monitoring, regulation. Coordination problems are hard (but not as hard as any form of AI alignment!). Coordination failures happen, so it would be wise to have a backup plan. Returning to value alignment as a possible path forward, I'll describe the math behind EigenBench, a pagerank-inspired approach to the problem of measuring AI values.

(V. Gorin): Dunkl differential-difference operators are one-parameter deformations of the usual derivative. 
First studied for their remarkable commutativity and their role in the Calogero-Moser-Sutherland 
quantum many-body system, they have recently found surprising applications in random matrix theory.
I will show how Dunkl operators can be used in the asymptotic analysis of random matrix eigenvalues, 
where Catalan numbers, the semicircle law, the Airy-beta line ensemble, and Tracy-Widom distributions 
naturally emerge.

(T. Lidman): A mathematical knot is simply a closed loop in space, but they show up in a variety of settings, ranging from algebraic geometry to biology.  We will discuss some foundational questions in knot theory, what tools can be used to study knots, and how they relate to various aspects of topology in dimensions 3 and 4. 

(G. Panova): Representation theoretic multiplicities are at the heart of many open problems in algebraic combinatorics. At the same time these quantities appear in Geometric Complexity Theory in the search for multiplicity obstructions for separating computational complexity classes like VP vs VNP. Most recently they have also been considered in quantum computing. In this talk we will introduce the objects and problems, explain how formalization through computational complexity theory could answer some of the open problems in the negative. We will also explain their role in GCT and quantum computing with a mixture of positive and negative answers.

(X. Zhou):

(J. Avigad):

(J. Rosenberg):

(S. Krushkal):

(J. Etnyre):

(L. Lin):

(J. Rivera-Letelier):

(T. Kucherenko):

(D. Barrett):

Past Ohio State University Mathematics Department Colloquia

• 2024-2025

• 2023-2024

• 2022-2023

• 2020-2021

• 2019-2020

• 2018-2019

• 2017-2018

• 2016-2017

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