Colloquium

1. Magic+Math conference activities

   When: Wed, December 31, 1969 - 7:00pm
   Where:
   
   

2. The Unitary Dual

   When: Wed, September 17, 2025 - 3:15pm
   Where: Kirwan Hall 3206
   Speaker: Jeffrey Adams (University of Maryland) - https://math.umd.edu/~jda/
   Abstract: Classifying the irreducible unitary representations of a Lie group (the Unitary Dual)  is a major problem with a long history. It is well known that the answer is complicated. The Atlas of Lie Groups and Representations project was started in 2002 with the goal of understanding the unitary dual using computational tools. In this talk I will describe a major result of this project: a description of the unitary dual. The answer is in terms of an algorithm which we have implemented in the atlas software, and recently used to compute the answer for E8. I will also discuss parallel efforts to understand the unitary dual conceptually, based on recent progress on Arthur's conjectures. These conjectures by Jim Arthur were first announced at a conference at the University of Maryland in 1983. This is joint work of the atlas project, whose members are listed at www.liegroups.org.
   

3. Common divisors of binomial coefficients and invariable generation of finite simple groups

   When: Wed, September 24, 2025 - 3:15pm
   Where: Kirwan Hall 3206
   Speaker: John Shareshian (Washington University ) - https://math.wustl.edu/people/john-shareshian
   Abstract: I will discuss joint work with Russ Woodroofe and joint work with Bob Guralnick and Woodroofe.  It follows quickly from a theorem of Kummer that, given an integer n>1, the greatest common divisor of the nontrivial binomial coefficeints {{n} \choose {k}}, k=1,2,...,n-1, is larger than 1 if and only if n is a prime power.  We considered the problem of finding the smallest number of primes such that each of these binomial coefficients is divisible by at least one of the chosen primes.
   
   This problem is closely related to the problem of invariable generation of alternating groups by Sylow subgroups - if there exist primes p and r such that A_n is generated by subgroups P and R whenever P is a Sylow p-subgroup and R is a Sylow r-subgroup, then one of p,r divides every nontrivial binomial coefficient.  
   
   This leads to similar questions: given a simple group G, can one find a pair (x,y) of elements of G such that g^{-1}xg and h^{-1}yh generate G for all g,h?  What if we put restrictions on the orders of x and y?
   
   I will discuss our progress on these problems and some motivation for our work.
   

4. Artificial Intelligence: Thinking, fast and slow

   When: Wed, October 1, 2025 - 3:15pm
   Where: Kirwan Hall 3206
   Speaker: Jim Yorke (University of Maryland) - https://www-math.umd.edu/people/faculty/item/528-yorke.html
   Abstract: I compare the ways humans and artificial intelligences think, building on Daniel Kahneman’s Systems 1 and 2 (Nobel Prize in Economics, 2002). System 1 is fast subconscious thought like recognizing a face, or walking, or other every-day tasks. System 2 is slow conscious analysis, like figuring out how I cross a mud puddle without soaking my shoes or searching through an audience to see if I know anyone. System 2 uses System 1 repeatedly. Talking and writing use System 2. I add a third component that I call System 3 — learning, improving both intuition (System 1) and analysis (System 2). All 3 components have explicit analogues in AIs. We can separate the roles of System 1 and 2 by comparing fast chess with slow chess. Fast chess allows 3 seconds per move which is essentially pure System 1 thought. Slow chess allows about 3 minutes per move, sixty times slower. Based on international chess ratings, I find that the best players at fast chess are the best at slow. Superb slow System 2 thinking is achieved only by chaining together superb intuitive System 1 insights. I give examples from mathematics and physics requiring System 1 intuition, including some from my new paper ``Tactics in Proofs", written with Boris Hasselblatt. I think AI needs the most improvement in its training System 2 for carrying out complex tasks, while humans may benefit greatly from improvement in the training of System 1, intuition.
   

5. Skipper (TBA)

   When: Wed, October 8, 2025 - 3:15pm
   Where: Kirwan Hall 3206
   Speaker: Rachel Skipper (University of Utah) -
   Abstract: TBA
   

6. Landscapes of harmonic maps (cancelled)

   When: Wed, December 3, 2025 - 3:15pm
   Where: Kirwan Hall 3206
   Speaker: Antoine Song (Caltech) - https://www.pma.caltech.edu/people/antoine-song
   Abstract: Harmonic maps from a surface to a target manifold are nonlinear analogue of harmonic functions. They form a fundamental class of objects in differential geometry, but most of the time, they are very hard to describe explicitly. In recent years, people have started to study their shape under "typical", "large" or "random" constraints. In this talk, I will give a biased survey of the developments in this field, which connect geometric analysis to dynamical systems and random matrix theory.
   

7. Ioana (TBA)

   When: Wed, February 4, 2026 - 3:15pm
   Where: Kirwan Hall 3206
   Speaker: Adrian Ioana (University of California, San Diego) - https://mathweb.ucsd.edu/~aioana/
   Abstract: TBA