
2:00 pm
Gregory Patchell  UCSD (gpatchel@ucsd.edu)
How to Maximize your Mean Ability
Food for Thought
APM 7321
AbstractIn this talk I will show you how to maximize your ameanability. More precisely, I will survey some results about maximal amenable subgroups and subalgebras and share a new result which states that it is possible for the space of maximal amenable extensions to be any ksimplex (such as a triangle!). While this talk will technically be about operator algebras, it will be accessible to anyone who knows a bit of group theory (semidirect products, free products, and the left regular representation).

4:00 pm
Prof. Samuel Shen  SDSU (sshen@sdsu.edu)
Some visualization tools for big climate data developed at the SDSU Climate Informatics Lab
Math 278C: Optimization and Data Science
APM 5829
AbstractSDSU Climate Informatics Lab has developed a suite of computer code and Apps for visualizing and delivering real climate data for the general public, such as school classrooms. This presentation will specifically demonstrate the following tools:
1. 4dimensional visual delivery (4DVD) of big climate data: www.4dvd.org.
2. Statistics, machine learning, and data visualization for climate science with R and Python: www.climatestatistics.org
3. Climate mathematics with R and Python: www.climatemathematics.org
4. 4DVD Rural Heat Island for a California Climate Action project: www.4dvdrhi.sdsu.edu
We will also discuss our proprietary database optimization algorithms for fast queries. Using cuttingedge database technologies and 3D video games, we will outline our product development for the NSF program of AI Institutes and NOAA National Centers for Environmental Information.

4:00 pm
Prof. Dragos Oprea  UCSD
The Chow ring of the moduli space of degree 2 K3 surfaces
Math 208: Seminar in Algebraic Geometry
APM 7321
AbstractI will discuss recent results describing the Chow rings and the tautological classes of the moduli space of quasipolarized K3 surfaces of degree 2. This is based on joint work with Samir Canning and Rahul Pandharipande.

3:00 pm
Dr. Lucas Buzaglo  UC San Diego
Universal enveloping algebras of infinitedimensional Lie algebras
Math 211A: Seminar in Algebra
APM 7321
AbstractUniversal enveloping algebras of finitedimensional Lie algebras are fundamental examples of wellbehaved noncommutative rings. On the other hand, enveloping algebras of infinitedimensional Lie algebras remain mysterious. For example, it is widely believed that they are never noetherian, but there are very few examples whose noetherianity is known. In this talk, I will summarize what is known about the noetherianity of enveloping algebras, with a focus on Lie algebras of derivations of associative algebras.

1:00 pm
Jasper Liu  UCSD
Matrix loci and orbit harmonics
Math 269: Combinatorics Seminar
APM 7321
AbstractLet $\mathrm{Mat}_{n \times n}(\mathbb{C})$ be the affine space of $n \times n$ complex matrices with coordinate ring $\mathbb{C}[{\mathbf x}_{n \times n}]$. We define graded quotients of $\mathbb{C}[{\mathbf x}_{n \times n}]$ where each quotient ring carries a group action. These quotient rings are obtained by applying the orbit harmonics method to matrix loci corresponding to the permutation matrix group $S_n$, the colored permutation matrix group $S_{n,r}$, the collection of all involutions in $S_n$, and the conjugacy classes of involutions in $S_n$ with a given number of fixed points. In each case, we explore how the algebraic properties of these quotient rings are governed by the combinatorial properties of the matrix loci. Based on joint work with Yichen Ma, Brendon Rhoades, and Hai Zhu.

2:00 pm
Miquel Ortega  Universitat Politecnica de Catalunya (UPC)
A canonical van der Waerden theorem in random sets
Math 269: Seminar in Combinatorics
APM 7321
AbstractThe canonical van der Waerden theorem states that, for large enough $n$, any colouring of $[n]$ gives rise to monochromatic or rainbow $k$APs. In joint work with Alvarado, Kohayakawa, Morris and Mota, we study sparse random versions of this result. More concretely, we determine the threshold at which the binomial random set $[n]_p$ inherits the canonical van der Waerden properties of $[n]$, using the container method.

4:00 pm
Brandon Alberts  Eastern Michigan University
Inductive methods for counting number fields
Math 209: Number Theory Seminar
APM 7321 and online (see https://www.math.ucsd.edu/~nts
/ )AbstractWe will discuss an inductive approach to determining the asymptotic number of Gextensions of a number field with bounded discriminant, and outline the proof of Malle's conjecture in numerous new cases. This talk will include discussions of several examples demonstrating the method.
[pretalk at 3:00PM]

10:00 am
Shreyasi Datta  University of York (shreyasi.datta@york.ac.uk)
Fourier Asymptotics and Effective Equidistribution
Math 211B: Group Actions Seminar
APM 7321
AbstractWe talk about effective equidistribution of the expanding horocycles on the unit cotangent bundle of the modular surface with respect to various classes of Borel probability measures on the reals, depending on their Fourier asymptotics. This is a joint work with Subhajit Jana.

11:00 am
Nikita Gladkov  UCLA (gladkovna@gmail.com)
Inequalities for connectivity events in Bernoulli percolation
Math 288: Probability & Statistics
APM 6402
AbstractIn Bernoulli percolation, events such as "two vertices are connected by an open path" naturally emerge. In this talk, I will explore the dependencies between these events for various vertex pairs and derive key FKGtype inequalities governing their probabilities and explain the relevance of these inequalities to the recent disproof of the Bunkbed Conjecture.

3:00 pm
Itamar Vigdorovich  UCSD
Character limits of arithmetic groups
Postdoc Seminar
APM 7218
AbstractIn the 1960s Thoma developed a theory of characters which generalizes the classical Fourier/Pontryagin theory of abelian groups, and at the same time Frobenius' theory on finite (and compact) groups.
After presenting the general theory, I will focus on arithmetic groups, or similarly, lattices in (semi)simple Lie groups, and tell about my work with Levit and Slutsky regarding the geometry/topology of the space of characters of such groups. Our main result is that for lattices in higher rank simple Lie groups (e.g for the group SL3(Z)), any sequence of distinct characters must converge pointwise to the dirac character at the identity. This implies character bounds of finite groups of Lie type (e.g SL3(Fp)).

4:00 pm
Denis Osin  Vanderbilt University
Generic Cayley graphs of countable groups
Math 295: Colloquium Seminar
APM 6402
AbstractDoes every infinite group admit a generating set such that the corresponding Cayley graph has infinite diameter? While there are examples of uncountable groups that fail to satisfy this property (e.g., the group of all permutations of the integers), the question for countable groups remains open. After reviewing the necessary background and some known results, I will discuss an attempt to solve this problem by choosing a random generating set. For a wide class of countable groups, this approach answers the question affirmatively and reveals a surprising phenomenon: random generating sets yield the same Cayley graph, independent of the group. Depending on the randomness model, this is either the familiar Rado graph (which has diameter 2) or a certain mysterious graph of infinite diameter.

2:00 pm
Finn Southerland  UCSD
Finn's Favorite Factorization Facts
Food for Thought
APM 7321
AbstractNot the factorizations you're thinking of! A 1factorization of a graph is a partition of its edges into perfect matchings. In this talk I hope to share some of the many questions about 1factorizations that I find interesting, explain how I came to care about a rather obscure fact, and prove it. Along the way we will draw some pretty pictures, of course. This talk should be totally accessible to anyone who has ever heard of graphs, and is based on collaboration with Michael Orrison and Rohan Chauhan.

3:00 pm
Professor Nicolas Monod  EPFL
The fixedpoint property and piecewiseprojective transformations of the line
Math 211A: Seminar in Algebra
APM 7321
AbstractWe describe a new and elementary proof of the fact that many groups of piecewiseprojective transformation of the line are nonamenable by constructing an explicit action without fixed points. One the one hand, such groups provide explicit counterexamples to the Dayvon Neumann problem. On the other hand, they illustrate that we can distinguish many "layers" of relative nonamenability between nested subgroups.

4:00 pm
Dr. Yee Ern Tan  Auburn University (yzt0060@auburn.edu)
Tensor decompositions with applications to LU and SLOCC equivalence of multipartite pure states
Math 278C: Optimization and Data Science
APM 6402
AbstractWe introduce a broad lemma, one consequence of which is the higher order singular value decomposition (HOSVD) of tensors defined by DeLathauwer, DeMoor and Vandewalle (2000). By an analogous application of the lemma, we find a complex orthogonal version of the HOSVD. Kraus's (2010) algorithm used the HOSVD to compute normal forms of almost all nqubit pure states under the action of the local unitary group. Taking advantage of the double cover SL2(C)×SL2(C)→SO4(C), we produce similar algorithms (distinguished by the parity of n) that compute normal forms for almost all nqubit pure states under the action of the SLOCC group.

4:00 pm
Linli Shi  University of Connecticut
On higher regulators of Picard modular surfaces
Math 209: Number Theory Seminar
APM 7321 and online (see https://www.math.ucsd.edu/~nts
/ )AbstractThe Birch and SwinnertonDyer conjecture relates the leading coefficient of the Lfunction of an elliptic curve at its central critical point to global arithmetic invariants of the elliptic curve. Beilinson’s conjectures generalize the BSD conjecture to formulas for values of motivic Lfunctions at noncritical points. In this talk, I will relate motivic cohomology classes, with nontrivial coefficients, of Picard modular surfaces to a noncritical value of the motivic Lfunction of certain automorphic representations of the group GU(2,1).

2:00 pm
Prof. Yi Zhao  Georgia State University (yzhao6@gsu.edu)
Extremal results in multipartite graphs
Math 269: Seminar in Combinatorics
APM 7321
AbstractClassical extremal results in graph theory (such as Turán's theorem) concern the maximal size of of a graph of given order and without certain subgraphs. Bollobás, Erdős, and Szemerédi in 1975 studied extremal problems in multipartite graphs. One of their problems (in its complementary form) was determining the maximal degree of a multipartite graph without an independent transversal. This problem has received considerable attention and was settle in 2006 (SzabóTardos and HaxellSzabó). Other questions asked by Bollobás, Erdős, and Szemerédi remain open, such as determining:
(1) the maximum degree in a multipartite graph without a partial independent transversal, and;
(2) the minimum degree that forces an octahedral graph in balanced tripartite graphs.In this talk I will survey recent progress on these and other related problems.