http://www-math.umd.edu/research/seminars.html http://www-math.umd.edu/research/seminars.html Wed, 17 Sep 2025 15:15:00 EDT 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.
]]> http://www-math.umd.edu/research/seminars.html Wed, 24 Sep 2025 15:15:00 EDT 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.
]]> http://www-math.umd.edu/research/seminars.html Wed, 01 Oct 2025 15:15:00 EDT 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.
]]> http://www-math.umd.edu/research/seminars.html Wed, 08 Oct 2025 15:15:00 EDT Where: Kirwan Hall 3206
Speaker: Rachel Skipper (University of Utah) -
Abstract: We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.
]]> http://www-math.umd.edu/research/seminars.html Wed, 03 Dec 2025 15:15:00 EST 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.
]]> http://www-math.umd.edu/research/seminars.html Wed, 04 Feb 2026 15:15:00 EST Where: Kirwan Hall 3206
Speaker: Adrian Ioana (University of California, San Diego) - https://mathweb.ucsd.edu/~aioana/
Abstract: TBA
]]> http://www-math.umd.edu/research/seminars.html Wed, 11 Feb 2026 15:15:00 EST Where: Kirwan Hall 3206
Speaker: Francois Golse (Douglis Memorial Lecture speaker) (École Polytechnique) - https://www.cmls.polytechnique.fr/perso/golse/
Abstract: Optimal transport is an old branch of the calculus of variations whose origins can be traced back to an important memoir of Monge in 1781, followed by remarkable contributions due to Kantorovich in 1942, and in the last 50 years by R.L. Dobrushin, Y. Brenier, and many others. Among the by-products of optimal transport is a family of distances metrizing the weak topology of Borel probability measures on Euclidean spaces. The analogy between Borel probability measures on phase space and the notion of density operators used in quantum mechanics suggests defining a notion of « pseudometric » which can be used to compare two (quantum) density operators, or a density operator with a probability density in phase space. The talk will discuss the main properties of this pseudometric, and compare them with the analogous results known for the optimal transport metrics defined for pairs of phase space probability densities.

This presentation is based on a series of works with E. Caglioti, C. Mouhot and T. Paul.
]]> http://www-math.umd.edu/research/seminars.html Wed, 18 Feb 2026 15:15:00 EST Where: Kirwan Hall 3206
Speaker: Eleanor Rieffel (NASA) - https://www.nasa.gov/people/eleanor-rieffel/
Abstract:  Quantum error correction is one of the most mature areas of quantum information processing. Nevertheless, major breakthroughs, including new families of codes, continue to be made. This talk will begin with a gentle introduction to quantum error correction, including some history (quantum error correction was initially thought to be impossible) and an overview of the powerful stabilizer operator formalism, with examples of stabilizer codes. I will move from stabilizer codes to subsystem codes, defining them generally and giving the Bacon-Shor subsystem codes as an example. From there, I will define a new and exciting type of code, dynamical, or Floquet, codes. I will describe the first such code, the honeycomb codes. In the second part of the talk, I will discuss recent work, joint with Sohaib Alam, on Dynamical Logical Qubits in the Bacon-Shor Code (PRA 2025). This work is part of a larger program in the field aiming to understand when one can define Floquet codes, when it is useful to do so, and subtilties with regard to defining their distance. The talk will conclude with the statement of some specific open problems.
]]> http://www-math.umd.edu/research/seminars.html Wed, 25 Feb 2026 15:15:00 EST Where: Kirwan Hall 3206
Speaker: Kiran Kedlaya (University of California San Diego) - https://kskedlaya.org/
Abstract: We classify all possible configurations of vectors in three-dimensional
space with the property that any two of the vectors form a rational
angle (measured in degrees). As a corollary, we find all tetrahedra
whose six dihedral angles are all rational. While these questions (and
their answers) are of an elementary nature, their resolution will take
us on a tour through cyclotomic number fields, computational algebraic
geometry, and an amazing fact about the geometry of tetrahedra
discovered by physicists in the 1960s. Joint work with Sasha Kolpakov,
Bjorn Poonen, and Michael Rubinstein.
]]> http://www-math.umd.edu/research/seminars.html Wed, 11 Mar 2026 15:15:00 EDT Where:

]]> http://www-math.umd.edu/research/seminars.html Wed, 08 Apr 2026 15:15:00 EDT Where: Kirwan Hall 3206
Speaker: Mahan Mj (Tata Institute of Fundamental Research) - https://mathweb.tifr.res.in/~mahan/
Abstract: A nearly hundred-year old question by Fatou asks for a synthesis of the following two kinds of holomorphic dynamical systems under a common framework of holomorphic correspondences on the Riemann sphere: (a) Kleinian groups acting on the Riemann sphere (b) iteration of complex polynomials on the Riemann sphere. Sullivan's dictionary gave us a way of translating techniques from one of these fields to give results in the other. In a relatively recent development, building on Sullivan's dictionary, a bridge has been built between these two classes in the spirit of Bers' simultaneous uniformization theorem. New holomorphic dynamical systems on the Riemann sphere have thus been discovered that arise as combinations or matings of Kleinian groups and polynomials. In some cases, these single valued matings give rise to multi-valued algebraic correspondences on the Riemann sphere, partially fulfilling Fatou's dream. A particular consequence of these constructions is an analog of the compactness theorem for Bers slices of punctured sphere groups. In 1982, Thurston posed a number of questions that guided the development of the theory of Kleinian groups for the next 3 decades. With the above analog of Bers compactness in place, many of these questions reincarnate themselves in this new context. We will survey some of these developments and questions. This is joint work with Yusheng Luo and Sabyasachi Mukherjee.
]]> http://www-math.umd.edu/research/seminars.html Wed, 22 Apr 2026 15:15:00 EDT Where: Kirwan Hall 3206
Speaker: Eric Katz (The Ohio State University ) - https://people.math.osu.edu/katz.60/
Abstract: In 1971, McMullen conjectured a characterization of the face numbers of convex simplicial polytopes. This conjecture, dubbed the “g-conjecture”, was resolved over the following ten years by work of Stanley and Billera–Lee. The extension of this conjecture to simplicial spheres remained open much longer. We will discuss the ingenious characteristic 2 proof given by Papadakis–Petrotou in 2020 and provide a unifying framework for it in commutative algebra. This is joint work in progress with Adiprasito, Oba, Papadakis, and Petrotou.
]]> http://www-math.umd.edu/research/seminars.html Wed, 29 Apr 2026 15:15:00 EDT Where: Kirwan Hall 3206
Speaker: Hans Wenzl (University of California at San Diego) - https://mathweb.ucsd.edu/~hwenzl/
Abstract: Vaughan Jones proved in the 1980s that the index of a subfactor of a von Neumann factor has to be in the set $\{ 4\cos^2 \pi/n,\ n=3,4,\ ...\ \}\cup [4,\infty]$. This turned out to be the tip of the iceberg of an incredibly rich structure. It has been realized for some time  that the classification of subfactors runs parallel to the classification of unitary tensor categories and their module categories. We review the current state of classification. This will include recent results about classification of module categories of an important class of fusion categories, closely related to Drinfeld-Jimbo quantum groups and loop groups.
]]> http://www-math.umd.edu/research/seminars.html Wed, 06 May 2026 15:15:00 EDT Where: Kirwan Hall 3206
Speaker: Srivatsav Kunnawalkam Elayavalli (UMD) - https://sites.google.com/view/srivatsavke/home
Abstract:   A countable group G is said to be a matricial field (MF) if it admits a ``strongly converging'' sequence of approximate homomorphisms into matrices, i.e, norms of polynomials converge to the corresponding value in the left regular representation. G is then said to be purely MF}(PMF) if this sequence of maps into matrices can be chosen as actual homomorphisms. G is further said to be purely finite field (PFF) if the image of each homomorphism is finite. These questions have phenomenal applications to the study of C* and von Neumann algebras, spectral geometry, random walks and random graphs, spectral gaps of hyperbolic manifolds, minimal surface theory and Yau's conjectures, and even applied mathematics including but not limited to signal processing.  
By developing a new operator algebraic approach to the MF problems, we are able to prove the following result bringing several new examples into the fold. Suppose G is a MF (resp., PMF, PFF) group and G is separable (i.e., 
\( H=\cap_{i\in \N}H_i \)
where 
\( H_i<G\) 
 are finite index subgroups) and K is a residually finite MF (resp., PMF, PFF) group. If either G or K is exact, then the amalgamated free product G*_{H}(H\times K) is MF (resp., PMF, PFF). Our work has several applications. Firstly, as a consequence of MF, the Brown--Douglas--Fillmore semigroups of many new reduced C*-algebras are not groups. Secondly, we obtain that arbitrary graph products of residually finite exact MF (resp., PMF, PFF) groups are MF (resp., PMF, PFF), yielding a significant generalization of the breakthrough work of Magee--Thomas. Thirdly, our work resolves the open problem of proving PFF for 3-manifold groups, more generally all RAAGs. Prior to our paper, PFF results remained unknown even in the simple subcase of free products. These results are of further significance since PFF is the property that is used in Antoine Song's approach towards the existence of minimal surfaces in spheres of negative curvature.
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