
11:00 am
Gaultier Lambert  University of Zurich
Normal approximation for traces of random unitary matrices
Math 288  Probability and Statistics
For zoom ID and password email: ynemish@ucsd.edu

11:00 am
Gunhee Cho  UCSB
The lower bound of the integrated Carath ÌeodoryReiffen metric and Invariant metrics on complete noncompact Kaehler manifolds
Math 258  Seminar in Differential Geometry
AP&M Room 7321
Zoom ID: 949 1413 1783AbstractWe seek to gain progress on the following longstanding conjectures in hyperbolic complex geometry: prove that a simply connected complete K Ìˆahler manifold with negatively pinched sectional curvature is biholomorphic to a bounded domain and the Carath ÌeodoryReiffen metric does not vanish everywhere. As the next development of the important recent results of D. Wu and S.T. Yau in obtaining uniformly equivalence of the base K Ìˆahler metric with the Bergman metric, the KobayashiRoyden metric, and the complete Ka ÌˆhlerEinstein metric in the conjecture class but missing of the Carath ÌeodoryReiffen metric, we provide an integrated gradient estimate of the bounded holomorphic function which becomes a quantitative lower bound of the integrated Carath ÌeodoryReiffen metric. Also, without requiring the negatively pinched holomorphic sectional curvature condition of the Bergman metric, we establish the equivalence of the Bergman metric, the KobayashiRoyden metric, and the complete Ka ÌˆhlerEinstein metric of negative scalar curvature under a bounded curvature condition of the Bergman metric on an ndimensional complete noncompact Ka Ìˆhler manifold with some reasonable conditions which also imply nonvanishing Carath ÌedoroyReiffen metric. This is a joint work with KyuHwan Lee.

11:00 am
Joshua Frisch  ENS Paris
The Infinite Conjugacy Class Property and its Applications in Random Walks and Dynamics
Department Colloquium
Zoom ID: 964 0147 5112
Password: ColloquiumAbstractA group is said to have the infinite conjugacy class (ICC) property if every nonidentity element has an infinite conjugacy class. In this talk I will survey some ideas in geometric group theory, harmonic functions on groups, and topological dynamics and show how the ICC property sheds light on these three seemingly distinct areas. In particular I will discuss when a group has only constant bounded harmonic functions, when every proximal dynamical system has a fixed point, and what this all has to do with the growth of a group. No prior knowledge of harmonic functions on groups or Topological dynamics will be assumed.
This talk will include joint work with Anna Erschler, Yair Hartman, Omer Tamuz, and Pooya Vahidi Ferdowsi.

12:00 pm
Sebastián Barbieri  Universidad de Santiago de Chile
Selfsimulable groups
Math 211B  Group Actions Seminar
Zoom ID 967 4109 3409
Email an organizer for the passwordAbstractWe say that a finitely generated group is selfsimulable if every action of the group on a zerodimensional space which is effectively closed (this means it can be described by a Turing machine in a specific way) is the topological factor of a subshift of finite type on said group. Even though this seems like a property which is very hard to satisfy, we will show that these groups do exist and that their class is stable under commensurability and quasiisometries of finitely presented groups. We shall present several examples of wellknown groups which are selfsimulable, such as Thompson's V and higherdimensional general linear groups. We shall also show that Thompson's group F satisfies the property if and only if it is nonamenable, therefore giving a computability characterization of this wellknown open problem. Joint work with Mathieu Sablik and Ville Salo.

2:00 pm
Petar Bakic  Utah
Howe Duality for Exceptional Theta Correspondences
Math 209  Number Theory Seminar
Pretalk at 1:20 PM
APM 6402 and Zoom;
See https://www.math.ucsd.edu/~nts/ AbstractThe theory of local theta correspondence is built up from two main ingredients: a reductive dual pair inside a symplectic group, and a Weil representation of its metaplectic cover. Exceptional correspondences arise similarly: dual pairs inside exceptional groups can be constructed using socalled Freudenthal Jordan algebras, while the minimal representation provides a suitable replacement for the Weil representation. The talk will begin by recalling these constructions. Focusing on a particular dual pair, we will explain how one obtains Howe duality for the correspondence in question. Finally, we will discuss applications of these results. The new work in this talk is joint with Gordan Savin.

2:00 pm
German Enciso  UC Irvine
Absolutely Robust Control Modules in Chemical Reaction Networks
Math 218  Seminars on Mathematics for Complex Biological Systems
Contact Bo Li at bli@math.ucsd.edu for the Zoom info
AbstractWe use ideas from the theory of absolute concentration robustness to control a species of interest in a given chemical reaction network. The results are based on the network topology and the deficiency of the system, independent of reaction parameter values. The control holds in the stochastic regime and the quasistationary distribution of the controlled species is shown to be approximately Poisson under a specific scaling limit.
https://mathweb.ucsd.edu/~bli/research/mathbiosci/MBBseminar/

4:00 pm
Andreas Buttenschoen  UBC
Bridging from single to collective cell migration with nonlocal particle interactions models
Department Colloquium
Zoom ID: 964 0147 5112
Password: ColloquiumAbstractIn both normal tissue and disease states, cells interact with one another, and other tissue components. These interactions are fundamental in determining tissue fates, and the outcomes of normal development, and cancer metastasis. I am interested in collective cell behaviours, which I view as swarms with a twist: (1) cells are not simply pointlike particles but have spatial extent, (2) interactions between cells go beyond simple attractionrepulsion, and (3) cells “live” in a regime where friction dominates over inertia. Examples include: wound healing, embryogenesis, the immune response, and cancer metastasis. In this seminar, I will give an overview of my computational, modelling, and theoretical contributions to tissue modelling at the subcellular, cellular, and population level.
In the first part, I focus on the nonlocal “Armstrong adhesion model” (Armstrong et al. 2006) for adhering tissue (an example of an aggregationdiffusion equation). Since its introduction, this approach has proven popular in applications to embyonic development and cancer modeling. However many mathematical questions remain. Combining global bifurcation results pioneered by Rabinowitz, equivariant bifurcation theory, and the mathematical properties of the nonlocal term, we prove a global bifurcation result for the nontrivial solution branches of the scalar Armstrong adhesion model. I will demonstrate how we used the equation’s symmetries to classify the solution branches by the nodal properties of the solution’s derivative.
In the second part, I focus on agentbased modelling of cell migration. Small GTPases, such as Rac and Rho, are well known central regulators of cell morphology and motility, whose dynamics play a role in coordinating collective cell migration. Experiments have shown GTPase dynamics to be affected by both spatiotemporally heterogeneous chemical and mechanical cues. While progress on understanding GTPase dynamics in single cells has been made, a major remaining challenge is to understand the role of GTPase heterogeneity in collective cell migration. Motivated by recent onedimensional experiments (e.g. microchannels) we introduce a onedimensional modelling framework allowing us to integrate cell biomechanics, changes in cell size, and detailed intracellular signalling circuits (reactiondiffusion equations). We use numerical simulations, and analysis tools, such as bifurcation analysis, to provide insights into the regulatory mechanisms coordinating collective cell migration.

10:30 am
Sergej Monavari  Utrecht University
Double nested Hilbert schemes and stable pair invariants
Math 208  Algebraic Geometry Seminar
Pretalk at 10:00 AM
Contact Samir Canning (srcannin@ucsd.edu) for zoom access.
AbstractHilbert schemes of points on a smooth projective curve are simply symmetric powers of the curve itself; they are smooth and we know essentially everything about them. We propose a variation by studying double nested Hilbert schemes of points, which parametrize flags of 0dimensional subschemes satisfying certain nesting conditions dictated by Young diagrams. These moduli spaces are almost never smooth but admit a virtual structure à la BehrendFantechi. We explain how this virtual structure plays a key role in (re)proving the correspondence between GromovWitten invariants and stable pair invariants for local curves, and say something on their Ktheoretic refinement.

10:00 am
Jurij Volcic  Copenhagen University
Ranks of linear pencils separate similarity orbits of matrix tuples
Math 243  Functional Analysis Seminar
Please email djekel@ucsd.edu for Zoom details
AbstractThe talk addresses the conjecture of Hadwin and Larson on joint similarity of matrix tuples, which arose in multivariate operator theory.
The main result states that the ranks of linear matrix pencils constitute a collection of separating invariants for joint similarity of matrix tuples, which affirmatively answers the twosided version of the said conjecture. That is, mtuples X and Y of n×n matrices are simultaneously similar if and only if rk L(X) = rk L(Y) for all linear matrix pencils L of size mn. Similar results hold for certain other group actions on matrix tuples. On the other hand, a pair of matrix tuples X and Y is given such that rk L(X) <= rk L(Y) for all L, but X does not lie in the closure of the joint similarity orbit of Y; this constitutes a counterexample to the general HadwinLarson conjecture.
The talk is based on joint work with Harm Derksen, Igor Klep and Visu Makam.

11:00 am
Andrew W Lawrie  MIT
The soliton resolution conjecture for equivariant wave maps
Math 248  Analysis Seminar
AbstractI will present joint work with Jacek Jendrej (CRNS, Sorbonne Paris Nord) on equivariant wave maps with values in the twosphere. We prove that every finite energy equivariant wave map resolves, as time passes, into a superposition of decoupled harmonic maps and radiation, settling the soliton resolution conjecture for this equation. It was proved in works of Côte, and Jia and Kenig, that such a decomposition holds along a sequence of times. We show the resolution holds continuouslyintime via a “noreturn” lemma based on the virial identity. The proof combines a collision analysis of solutions near a multisoliton configuration with concentration compactness techniques. As a byproduct of our analysis we also prove that there are no elastic collisions between pure multisolitons.

2:30 pm
Cheng Li  UCSD
The Thick Subcategory Theorem
Math 292  Topology Seminar (student talk series on chromatic homotopy theory)

11:00 am
Xiaolong Li  Wichita
Curvature operator of the second kind and proof of Nishikawa's conjecture
Math 258  Seminar of Differential Geometry
AP&M Room 7321
Zoom ID: 949 1413 1783
AbstractIn 1986, Nishikawa conjectured that a closed Riemannian manifold with positive curvature operator of the second kind is diffeomorphic to a spherical space form and a closed Riemannian manifold with nonnegative curvature operator of the second kind is diffeomorphic to a Riemannian locally symmetric space. Recently, the positive case of Nishikawa's conjecture was proved by CaoGurskyTran and the nonnegative case was settled by myself. In this talk, I will first talk about curvature operators of the second kind and then present a proof of Nishikawa's conjecture under weaker assumptions.

12:00 pm
Julien Melleray  Université Lyon 1
From invariant measures to orbit equivalence, via locally finite groups
Math 211B  Group Actions Seminar
Zoom ID: 967 4109 3409
Email an organizer for the passwordAbstractA famous theorem of Giordano, Putnam and Skau (1995) states that two minimal homeomorphisms of a Cantor space X are orbit equivalent (i.e, the equivalence relations induced by the two associated actions are isomorphic) as soon as they have the same invariant Borel probability measures. I will explain a new "elementary" approach to prove this theorem, based on a strengthening of a result of Krieger (1980). I will not assume prior familiarity with Cantor dynamics. This is joint work with S. Robert (Lyon).

2:00 pm
Johnatan (Yonatan) Aljadeff  Neurobiology, UCSD
Multiplicative Shot Noise: A New Route to Stability of Plastic Networks
Math 218  Seminars on Mathematics for Complex Biological Systems
Contact Bo Li at bli@math.ucsd.edu for the Zoom info
AbstractFluctuations of synapticweights, among many other physical, biological and ecological quantities, are driven by coincident events originating from two 'parent' processes. We propose a multiplicative shotnoise model that can capture the behavior of a broad range of such natural phenomena, and analytically derive an approximation that accurately predicts its statistics. We apply our results to study the effects of a multiplicative synaptic plasticity rule that was recently extracted from measurements in physiological conditions. Using meanfield theory analysis and network simulations we investigate how this rule shapes the connectivity and dynamics of recurrent spiking neural networks. We show that the multiplicative plasticity rule, without finetuning, gives a stable, unimodal synapticweight distribution with a large fraction of strong synapses. The strong synapses remain stable over long times but do not `run away'. Our results suggest that the multiplicative plasticity rule offers a new route to understand the tradeoff between flexibility and stability in neural circuits and other dynamic networks. Joint work with Bin Wang.
https://mathweb.ucsd.edu/~bli/research/mathbiosci/MBBseminar/