Sunday,
May 12 |
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Monday,
May 13 |
- 10:00–11:00 Professional Development Seminar, Kemeny 343 and on Zoom
 
- A career in math and data
- Jean Steiner, Google
- I will give a short overview of how my career has evolved from pure mathematician to data scientist and I will share some of my favorite pieces of career advice. Then I will give a few flavors of some of the projects data scientists at Google might work on. I will aim to leave lots of time for questions!
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Tuesday,
May 14 |
- 14:25–15:25 Algebra and Number Theory Seminar, Kemeny 343
- Galois representations attached to CM elliptic curves and their applications
- Alvaro Lozano-Robledo, University of Connecticut
- In this talk we will discuss several applications of a recent classification of $\ell$-adic Galois representations attached to CM elliptic curves: computing adelic images attached to CM elliptic curves, maximal abelian extensions in their division fields, and models of CM elliptic curves with a given $\ell$-adic Galois representation. These are ongoing projects in collaboration with Enrique González-Jiménez (UAM), Asimina Hamakiotes (UConn), and Benjamin York (UConn).
- 14:30–15:30 Applied and Computational Mathematics Seminar, Kemeny 307
- How AI Aggregators Affect Knowledge Sharing
- James Siderius, Dartmouth College
- Recent advancements in AI have brought great promise to more efficiently aggregate and deliver information, but also raise concerns about their tendency to exacerbate existing biases entrenched in society. In this talk, we formalize this tradeoff by extending the DeGroot model of network learning to incorporate AI aggregators. We model these aggregators as nodes in the network that take as input beliefs from the population (“training data”) and communicate synthesized beliefs (“answers to queries”). We show that the feedback loop between AI input and output tends to amplify the majority opinion, a phenomenon known as model collapse, and can degrade the quality of information sharing in equilibrium under some mild conditions. In doing so, we also contrast the case of a single global aggregator (e.g., ChatGPT) to many local aggregators (e.g., Internet forums) to provide general conditions under which AI aggregators help or hinder wisdom in society. This is joint work with Daron Acemoglu, Darren Lin, and Asuman Ozdaglar.
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Wednesday,
May 15 |
- 18:00 ⋆ Kemeny Lecture ⋆, Kemeny 008
- How to get to the moon playing the 15 puzzle
- Anne Schilling, UC Davis
- Probability is the mathematical study of how likely an event occurs or a proposition is true. Representation theory
is the study of algebraic structures by realizing their elements as linear maps on vector spaces or modules
and decomposing them into their smallest constituents. Both probability and representation theory lend themselves to combinatorial analysis.
In this talk we explore how to exploit combinatorial tools (similar to the 15 puzzle) to answer deep questions in probability and representation
theory, in particular those that helped to get mankind to the moon.
- Poster
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Thursday,
May 16 |
- 15:15 ⋆ Kemeny Lecture ⋆, Kemeny 007
- The ubiquity of crystal bases
- Anne Schilling, UC Davis
- Crystal bases are combinatorial skeletons of Lie algebra representations. They appeared in the work of Kashiwara, Lusztig and Littelmann on quantum groups and the geometry of flag varieties. Crystal bases arise in many unexpected places, from mathematical physics to probability and number theory. In this talk, I will showcase ten reasons and applications of how crystal theory can be used to solve problems in representation theory, geometry and beyond.
- Poster
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Friday,
May 17 |
- 15:15 ⋆ Kemeny Lecture ⋆, Kemeny 307
- From quasi-symmetric to Schur expansions via the inverse quasi-Kostka matrix
- Anne Schilling, UC Davis
- It is an important problem in algebraic combinatorics to deduce the Schur function expansion of a symmetric function, whose
expansion in terms of the fundamental quasisymmetric function is known. For example,
formulas are known for the fundamental expansion of a Macdonald symmetric function and for the plethysm of two
Schur functions, while the Schur expansions of these expressions are still elusive.
Egge, Loehr and Warrington provided a method to obtain the Schur expansion
from the fundamental expansion by replacing each quasisymmetric function by a Schur function
(not necessarily indexed by a partition) and using straightening rules to obtain the Schur
expansion. Here we provide a new method which only involves the coefficients of the quasisymmetric functions
indexed by partitions and the quasi-Kostka matrix. As an application, we prove the lexicographically largest term
in the Schur expansion of the plethysm of two Schur functions and the Schur expansion of $s_w[s_h](x,y)$ for $w=2,3,4$
using novel symmetric chain decompositions of Young's lattice for partitions in a $w\times h$ box.
This is based on joint work with Rosa Orellana, Franco Saliola and Mike Zabrocki.
- Poster
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Saturday,
May 18 |
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