Abstract: Ensembles are widely used, with demonstrated value. They are believed to sample a small subspace where error preferentially falls; with a much lower error in their mean, to contain genuinely more information about future weather; and with case-dependent variations in their distribution and cloud, to enhance probabilistic forecast performance and capture the dynamical evolution of the real atmosphere. Instead, an analysis of operational, perfect, and statistically generated ensembles reveal a different picture. This talk will provide a review of ensemble forecasting from both theoretical and operational perspectives.
Abstract: Quiver Donaldson-Thomas invariants are integers determined by the geometry of moduli spaces of quiver representations. They play an important role in the description of BPS states of supersymmetric quantum field theories. I will describe a correspondence between quiver Donaldson-Thomas invariants and Gromov-Witten counts of rational curves in toric and cluster varieties. This is joint work with Hulya Arguz (arXiv:2302.02068 and arXiv:arXiv:2308.07270).
Abstract: The linear assignment problem is a fundamental problem in combinatorial optimization with a wide range of applications, from operational research to data sciences. It consists of assigning ``agents" to ``tasks" on a one-to-one basis, while minimizing the total cost associated with the assignment. While many exact algorithms have been developed to identify such an optimal assignment, most of these methods are computationally prohibitive for large size problems.In this talk, I will describe a novel approach to solving the assignment problem using techniques adapted from statistical physics.In particular I will derive a strongly concave effective free energy function that captures the constraints of the assignment problem at a finite temperature. This free energy decreases monotonically as a function of beta, the inverse of temperature, to the optimal assignment cost, providing a robust framework for temperature annealing. For large enough beta values the exact solution to the generic assignment problem can be derived using a simple round-off to the nearest integer of the elements of the computed assignment matrix. I will also describe a provably convergent method to handle degenerate assignment problems. Finally, I will describe computer implementations of this framework that are optimized for parallel architectures, one based on CPU, the other based on GPU.These implementations enable solving large assignment problems (of the orders of a few 10000s) in computing clock times of the orders of minutes.
Abstract: The commensurator of a group consists of isomorphisms between its finite index subgroups. Geometrically, the commensurator encodes isometries between finite covers of a Riemannian manifold. I will discuss a question raised independently by Greenberg and Shalom: Can an infinite discrete subgroup of a simple Lie group have dense commensurator and not be a lattice? I will explain the surprising connections between this question and other long-standing open problems, and discuss recent progress on special cases of the question. This is joint work with (subsets of) Brody, Fisher, and Mj.
Abstract: In this talk, I present recent work on stochastic fluid-structure interaction systems involving the coupled dynamics of fluids interacting with elastic structures under the additional influence of stochastic (random) effects. Fluid-structure interaction arises in real-life applications to biomedical, civil, and mechanical engineering, and there has been recent interest in quantifying and understanding the impact of stochastic effects on coupled fluid-structure dynamics. I will focus on a well-posedness result for a stochastic fully coupled fluid-structure system describing the dynamics of a Stokes flow through a channel with elastic walls, under the additional influence of stochastic forcing in time. We will discuss a constructive existence proof which employs an operator splitting scheme to semi-discretize the full problem in order to construct approximate solutions. We then discuss how to use methods from both fluid-structure interaction and stochastic PDEs in order to pass to the limit in the approximate solutions. This methodology provides a robust mathematical framework for analyzing a variety of complex fully coupled stochastic systems of interest in fluid-structure interaction. This is joint work with Sunčica Čanić at University of California, Berkeley.
Abstract: Many inexperienced long-distant bird, insect and turtle migrants reach remote non-breeding destinations independently, using inherited geomagnetic or celestial compass cues. Inexperienced migrants are also proposed to detour unfavorable regions using inherited geomagnetic signposts to trigger switches in migratory headings (Zugknicks). However, the overall relative feasibility among migratory compass courses and signposts (often termed clock-and-compass migration) remains uncertain, particularly at population levels. To address these unknowns, I developed a compass-based migration model incorporating spatiotemporal geomagnetic data (1900-2023) and an evolutionary algorithm, accounting for trans-generational changes in inherited geomagnetic headings and signposts through population mixing and natal dispersal. Signposted trans-hemispheric songbird migrations remained viable over the 124-year period, including through a highly geomagnetically unstable region (East-arctic North America and Greenland) and across a migratory divide maintained through dominant allelic inheritance. The key role of intrinsic variability in inheritance of headings is also discussed. Finally, I discuss how migratory orientation programs could both mediate and constrain evolution of routes in response to global climate change.
Abstract: Obstruction bundle gluing is a technique which can be used for the foundations of topological invariants that count holomorphic curves (or solutions to other PDEs) in situations where transversality fails, but not too badly. This talk will give an introduction to obstruction bundle gluing and work out a simple example that arises in defining embedded contact homology (the simplest nontrivial case of proving that the differential squares to zero). Based on joint work with Cliff Taubes.
Abstract: In this talk, we will discuss the results of the 2023 Towson University REU on indivisibility of classes of finite graphs. We will first consider indivisibility for hereditarily sparse graphs. Then we will turn our attention to a number of classes of graphs which are characterized by forbidden induced subgraphs, including cographs and perfect graphs. This is joint work with Vince Guingona, Felix Nusbaum, Zain Padamsee, Christian Pippin, and Ava Zinman.
Abstract: We present accurate and efficient numerical methods to simulate the de- formation of drops and bubbles in Stokes flow with surfactant. The majority of the talk will focus on a ‘hybrid’ or multiscale numerical method devel- oped over several years to address difficulties in the numerical computation of fluid interfaces with soluble surfactant, which advects and diffuses in fluids and adsorbs/desorbs from interfaces. In the physically representative large Peclet number limit, a thin transition layer develops near an interface in which physical quantities rapidly vary, yet must be well resolved for accurate computation of interface dynamics. The hybrid method uses the slenderness of the layer to incorporate a separate analytical reduction of the layer’s dy- namics into a novel boundary integral formulation. We present several recent developments, including a fast mesh-free algorithm for resolving the transi- tion layer, and a method which captures the transfer of surfactant between the exterior and interior fluid via transport through the combined interface- transition layer structure.
Abstract: Arthur conjectured the existence of sets of representations of a real reductive group satisfying various properties. A definition of these "Arthur packets" was given in 1992 by Adams, Barbasch and Vogan. They proved all of the conjectural properties with the significant exception of the fact these representations are unitary.
Unitarity of "unipotent" packets is known: by work of Barbasch/Sun/Ma/Zhu for classical groups (a series of arXiv papers), for classical groups, and Adams/Miller/Vogan for exceptional groups (using the Atlas software). The general case reduces to the unipotent case. This requires a generalization of endoscopic lifting, which includes both real and cohomological induction.
Abstract: Let S be a subset of the Boolean cube that is both an antichain and a distance-2r+1 code. How large can S be? I will describe the answer to this question and link it to combinatorial proofs of anticoncentration inequalities for sums of random variables. Joint work with Xiaoyu He, Bhargav Narayanan, and Sam Spiro.
Abstract: The walk-on-spheres (WoS) method is a monte-carlo technique for solving PDEs. First developed by Muller in 1956, it has seen a recent resurgence in computer graphics as it allows for problems to be solved on complicated geometries without the need for meshing. The main theoretical tool behind WoS relies on the stochastic process interpretation of solutions of boundary value problems. In this talk, the basics of the walk-on-spheres method will be discussed, its advantages & disadvantages, as well as some applications.
Abstract: We study skew products with base being symmetric interval exchange transformations. We show that if the cocycle is either logarithmic and odd on each of the exchanged intervals or it is given by a shifted indicator of (0,1/2), the the skew product is ergodic. This result is based on a joint work with Frank Trujillo and Corinna Ulcigrai.
Abstract: The lecture will present elements from early history and make references to some of the giants in quantum computation, starting with Richard Feynman and Yuri Manin. It will then give a picture of the State of the Art today as far as available hardware is concerned after introducing some basic concepts: qubit, measurement, superposition and entanglement.
During his lifetime, Feynman (an American theoretical physicist) became one of the best known scientists in the world. Yuri Manin (a Russian mathematician) was known for work in algebraic geometry and diophantine geometry. Both of them independently advocated the idea of "computation grounded in physics", which led to the modern concept of quantum computation and the idea of storing and processing information.
The involvement of Mathematicians has been crucial since the beginning of quantum information science. It was another mathematician Peter Shor who in 1994 discovered a polynomial-time algorithm for factoring numbers igniting a flurry of activity that created the field of quantum information.
Coffee and snacks will be provided RSVP appreciated at: https://forms.gle/jYUa1v1NPN5VPyQs5
Abstract: I will present joint work with Jacek Jendrej. We consider classical scalar fields in dimension 1+1 with a symmetric double-well self-interaction potential. Examples of such equations are the phi-4 model and the sine-Gordon equation. Such equations admit non-trivial static solutions called kinks and antikinks. A kink cluster is a solution approaching, for large positive times, a superposition of alternating kinks and antikinks whose velocities converge to zero and mutual distances grow to infinity. Our main result is a determination of the leading order asymptotic behavior of any kink cluster. Our results are partially inspired by the notion of "parabolic motions" in the Newtonian n-body problem. We explain this analogy and its limitations. We also explain the role of kink clusters as universal profiles for the formation/annihilation of multikink configurations.
Abstract: Ever since the last ice age, when children wandered out of their frozen caves and made Moebius bands from strips of paper, humans have wondered how short a strip of paper they could use to make such Moebius bands. In this talk I will give a hands-on and elementary account of my recent solution of the optimal paper Moebius band conjecture of B. Halpern and C. Weaver from 1977. My result is that a unit width strip of paper needs to be more than sqrt(3) units long in order for you to be able to twist it up into a paper Moebius band, and the bound is sharp.
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