Thu, Jan 27 2022
  • 11:00 am
    Gunhee Cho - UCSB
    The lower bound of the integrated Carath ́eodory-Reiffen metric and Invariant metrics on complete noncompact Kaehler manifolds

    Math 258 - Seminar in Differential Geometry

    AP&M Room 7321
    Zoom ID: 949 1413 1783

    We seek to gain progress on the following long-standing conjectures in hyperbolic complex geometry: prove that a simply connected complete K ̈ahler manifold with negatively pinched sectional curvature is biholomorphic to a bounded domain and the Carath ́eodory-Reiffen 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 ̈ahler metric with the Bergman metric, the Kobayashi-Royden metric, and the complete Ka ̈hler-Einstein metric in the conjecture class but missing of the Carath ́eodory-Reiffen metric, we provide an integrated gradient estimate of the bounded holomorphic function which becomes a quantitative lower bound of the integrated Carath ́eodory-Reiffen metric. Also, without requiring the negatively pinched holomorphic sectional curvature condition of the Bergman metric, we establish the equivalence of the Bergman metric, the Kobayashi-Royden metric, and the complete Ka ̈hler-Einstein metric of negative scalar curvature under a bounded curvature condition of the Bergman metric on an n-dimensional complete noncompact Ka ̈hler manifold with some reasonable conditions which also imply non-vanishing Carath ́edoroy-Reiffen metric. This is a joint work with Kyu-Hwan 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: Colloquium 

    A group is said to have the infinite conjugacy class (ICC) property if every non-identity 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
    Self-simulable groups

    Math 211B - Group Actions Seminar

    Zoom ID 967 4109 3409
    Email an organizer for the password

    We say that a finitely generated group is self-simulable if every action of the group on a zero-dimensional 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 quasi-isometries of finitely presented groups. We shall present several examples of well-known groups which are self-simulable, such as Thompson's V and higher-dimensional general linear groups. We shall also show that Thompson's group F satisfies the property if and only if it is non-amenable, therefore giving a computability characterization of this well-known 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

    Pre-talk at 1:20 PM

    APM 6402 and Zoom;
    See https://www.math.ucsd.edu/~nts/

    The 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 so-called 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

    We 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 non-local particle interactions models

    Department Colloquium

    Zoom ID:   964 0147 5112
    Password: Colloquium

    In 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 point-like particles but have spatial extent, (2) interactions between cells go beyond simple attraction-repulsion, 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 sub-cellular, 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 aggregation-diffusion 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 non-local term, we prove a global bifurcation result for the non-trivial 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 agent-based 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 spatio-temporally 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 one-dimensional experiments (e.g. microchannels) we introduce a one-dimensional modelling framework allowing us to integrate cell bio-mechanics, changes in cell size, and detailed intra-cellular signalling circuits (reaction-diffusion equations). We use numerical simulations, and analysis tools, such as bifurcation analysis, to provide insights into the regulatory mechanisms coordinating collective cell migration.

Fri, Jan 28 2022
  • 10:30 am
    Sergej Monavari - Utrecht University
    Double nested Hilbert schemes and stable pair invariants

    Math 208 - Algebraic Geometry Seminar

    Pre-talk at 10:00 AM

    Contact Samir Canning (srcannin@ucsd.edu) for zoom access.

    Hilbert 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 0-dimensional subschemes satisfying certain nesting conditions dictated by Young diagrams. These moduli spaces are almost never smooth but admit a virtual structure à la Behrend-Fantechi. We explain how this virtual structure plays a key role in (re)proving the correspondence between Gromov-Witten invariants and stable pair invariants for local curves, and say something on their K-theoretic refinement.

Tue, Feb 1 2022
  • 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

    The 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 two-sided version of the said conjecture. That is, m-tuples 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 counter-example to the general Hadwin-Larson 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

    I will present joint work with Jacek Jendrej (CRNS, Sorbonne Paris Nord) on equivariant wave maps with values in the two-sphere. 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 continuously-in-time via a “no-return” lemma based on the virial identity. The proof combines a collision analysis of solutions near a multi-soliton configuration with concentration compactness techniques. As a byproduct of our analysis we also prove that there are no elastic collisions between pure multi-solitons. 

Thu, Feb 3 2022
  • 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

    In 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 Cao-Gursky-Tran 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 password

    A 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

    Fluctuations of synaptic-weights, among many other physical, biological and ecological quantities, are driven by coincident events originating from two 'parent' processes. We propose a multiplicative shot-noise 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 mean-field 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 fine-tuning, gives a stable, unimodal synaptic-weight 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/