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  • Ramification Theory for Arbitrary Valuation Rings in Positive Characteristic. - Algebra-Number Theory

    Speaker: Vaidehee Thatte (Queen's University, Ontario, Canada) - http://mast.queensu.ca/~vaidehee/Abstract: In classical ramification theory, we consider extensions of complete discrete valuation rings with perfect residue fields. We would like to studyarbitrary valuation rings with possibly imperfect residue fields and possiblynon-discrete valuations of rank >=1, since many interesting complicationsarise for such rings. In particular, defect may occur (i.e. we can have anon-trivial extension, such that there is no extension of the residue field orthe value group).We present some new results for Artin-Schreier extensions of arbitraryvaluation fields in positive characteristic p. These results relate the \higherramification ideal" of the extension with the ideal generated by the inversesof Artin-Schreier generators via the norm map. We also introduce a general-ization and further refinement of Kato's refined Swan conductor in this case.Similar results are true in mixed characteristic (0; p).

    When: Mon, February 19, 2018 - 2:00pm
    Where: Kirwan Hall 3206

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    Abstract: In classical ramification theory, we consider extensions of complete discrete valuation rings with perfect residue fields. We would like to studyarbitrary valuation rings with possibly imperfect residue fields and possiblynon-discrete valuations of rank >=1, since many interesting complicationsarise for such rings. In particular, defect may occur (i.e. we can have anon-trivial extension, such that there is no extension of the residue field orthe value group).We present some new results for Artin-Schreier extensions of arbitraryvaluation fields in positive characteristic p. These results relate the \higherramification ideal" of the extension with the ideal generated by the inversesof Artin-Schreier generators via the norm map. We also introduce a general-ization and further refinement of Kato's refined Swan conductor in this case.Similar results are true in mixed characteristic (0; p).
  • Measures of Measures and PDEs in Infinite Dimensions - RIT on Applied PDE

    Speaker: Pierre-Emmanuel Jabin (University of Maryland) -

    When: Mon, February 19, 2018 - 3:00pm
    Where: Kirwan Hall 1311

    View Abstract

    Abstract: http://www.terpconnect.umd.edu/~lvrmr/2017-2018-S/Classes/RIT.shtml
  • Hyperbolic surfaces as singular flat surfaces - Geometry-Topology

    Speaker: Aaron Feynes (University of Toronto) - http://www.math.toronto.edu/afenyes/

    When: Mon, February 19, 2018 - 3:15pm
    Where: Kirwan Hall 3206

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    Abstract: It's long been known that a hyperbolic surface with a maximal measured geodesic lamination is the same thing, loosely speaking, as a half-translation surface: a singular flat surface with a geodesic foliation. I say "loosely" to mean that corresponding hyperbolic and half-translation surfaces are only identified up to isotopy. I'll present a tighter version of this correspondence, due to Gupta, which maps each hyperbolic surface to its corresponding half-translation surface in a geometrically rigid way. This mapping turns the nonabelian flat bundle encoding the hyperbolic structure into the abelian flat bundle encoding the half-translation structure, carrying out a concrete instance of Gaiotto, Hollands, Moore, and Neitzke's abelianization process.
  • Morphisms in categories of nonlocal games (cont'd) - RIT on Quantum Information

    Speaker: Brad Lackey (University of Maryland) - http://www.umiacs.umd.edu/~bclackey

    When: Mon, February 19, 2018 - 4:15pm
    Where: Atlantic 3100A

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    Abstract: Synchronous correlations are a class of nonlocal games that behave like functions between finite sets. We examine categories whose morphisms are games with synchronous classical, quantum, or general nonsignaling correlations, characterizing when morphisms in these categories are monic, epic, sections, or retractions.
  • Progress in the Riemann-Hilbert correspondence (note the unusual time) - Geometry-Topology

    Speaker: Andy Neitzke (University of Texas) - https://www.ma.utexas.edu/users/neitzke/Abstract: Given a linear ordinary differential equation in one complex variable z, e.g. a "Schrodinger equation" (d2 / dz2 + P(z)) f(z) = 0, one  would like to understand the solutions as well as possible. One concrete question is: what is the monodromy of the solutions when z goes around a loop? I will describe a conjectural scheme for solving this problem, which gives more precise information than was previously available, and which connects the problem to various other areas such as the combinatorics of cluster algebras, the theory of enumerative invariants (generalized Donaldson-Thomas invariants of 3-Calabi-Yau categories), and the geometry of trajectories of quadratic differentials (and higher analogues).

    When: Tue, February 20, 2018 - 10:00am
    Where: Kirwan Hall 3206

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    Abstract: Given a linear ordinary differential equation in one complex variable z, e.g. a "Schrodinger equation" (d2 / dz2 + P(z)) f(z) = 0, one  would like to understand the solutions as well as possible. One concrete question is: what is the monodromy of the solutions when z goes around a loop? I will describe a conjectural scheme for solving this problem, which gives more precise information than was previously available, and which connects the problem to various other areas such as the combinatorics of cluster algebras, the theory of enumerative invariants (generalized Donaldson-Thomas invariants of 3-Calabi-Yau categories), and the geometry of trajectories of quadratic differentials (and higher analogues).
  • Model Theory Reading Seminar - Logic

    Speaker: Vince Guingona (Towson University) -

    When: Tue, February 20, 2018 - 2:00pm
    Where: Kirwan Hall 1311

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    Abstract: We continue our reading of ``Regularity lemmas for distal structures."
  • Heat diffusion on inverse limit spaces - Norbert Wiener Center

    Speaker: Patricia Alonso Ruiz (U Conn) -

    When: Tue, February 20, 2018 - 2:00pm
    Where: Kirwan Hall 3206

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    Abstract: Inverse (or projective) limits give rise to a wide range of spaces that
    can show remarkably different properties. The present talk aims to illustrate
    how different the (in some sense natural) diffusion processes occurring on them
    can be by looking at two examples: a parametric family of diamond fractals
    and pattern spaces of aperiodic Delone sets.

    On a generalized diamond fractal, a canonical diffusion process can be con-
    structed following a procedure proposed by Barlow and Evans for inverse lim-
    its of metric measure spaces. The associated heat semigroup has a kernel, of

    which many properties have been studied by Hambly and Kumagai in the case
    of constant parameters. It turns out that in general it is possible to give a
    rather explicit expression of the heat kernel, that is in particular uniformly
    continuous and admits an analytic continuation.
    In contrast, pattern spaces feature quite an opposite scenario. Regarded as
    compact metric measure spaces of a suitable type, one can introduce a diffusion
    process with an especially simple expression whose associated heat semigroup
    has no density, that is a heat kernel, with respect to the natural measure of
    the space.
  • Independence in generic expansions and fusions - Logic

    Speaker: Alex Kruckman (Indiana University) -

    When: Tue, February 20, 2018 - 3:30pm
    Where: Kirwan Hall 1311

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    Abstract: The word "generic" is often applied to a theory T* when it arises as a model companion of a base theory T. Generic theories exhibit lots of "random" behavior, so they are rarely stable or NIP, but they can sometimes be shown to be simple by characterizing a well-behaved notion of independence in T* (namely non-forking independence) in terms of independence in T. Recently, there has been increased interest in the property NSOP1, a generalization of simplicity, spurred by the work of Chernikov, Kaplan, and Ramsey, who showed that NSOP1 theories can also be characterized by the existence of a well-behaved notion of independence (namely Kim independence). In this talk, I will present a number of preservation results for simplicity and NSOP1 under generic constructions. In joint work with Nicholas Ramsey, generic expansion and generic Skolemization: add new symbols to the language, interpreted arbitrarily or as Skolem functions, and take the model companion. And in very recent results towards a joint project with Minh Chieu Tran and Erik Walsberg, interpolative fusion: given an L_1-theory T_1 and and L_2-theory T_2, which intersect in an L_0-theory T_0, take the model companion of the union of T_1 and T_2.
  • Nonconforming Finite Element Methods for High Order Elliptic Equations in $\mathbb{R}^n$ - Numerical Analysis

    Speaker: Shuonan Wu (Penn State University) - http://www.personal.psu.edu/sxw58/

    When: Tue, February 20, 2018 - 3:30pm
    Where: Kirwan Hall 3206

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    Abstract: In this talk, we propose two families of nonconforming finite element methods for 2m-th order elliptic equations in $\mathbb{R}^n$ on simplicial grids. Both of them naturally extend the methods proposed by Wang and Xu [Math. Comp. 82(2013), pp. 25--43], where m = 0, n >= 1, introduces some interior penalty terms to the bilinear form when $m > n$. The shape function space of nonconforming element consists of all polynomials with a degree not greater than m and is hence minimal. The nonconforming finite element spaces have some natural inclusion properties as in the corresponding Sobolev spaces in the continuous cases. We establish quasi-optimal error estimates in the energy norm for both of them, provided that the corresponding conforming relatives exist. These theoretical results are further validated by the numerical tests. Besides, we propose an $H^3$ nonconforming finite element that is robust for the sixth order singularly perturbed problems in 2D, which is of practical interest to the mathematical models containing small parameters.
  • The T^i functors - Student Algebraic Geometry Seminar

    Speaker: Yousheng Shi (UMD) -

    When: Tue, February 20, 2018 - 3:30pm
    Where: Math 0104
  • False Discovery Rates - RIT on Statistics

    Speaker: Yunjiang Ge (STAT Program) -

    When: Tue, February 20, 2018 - 4:00pm
    Where: MTH 1313
  • The dilogarithm function and hyperbolic volume - Student Geometry and Topology

    Speaker: Laura Iosip () -

    When: Wed, February 21, 2018 - 1:00pm
    Where: Kirwan Hall 1310
  • Boundary layers and the vanishing viscosity limit in incompressible flows - CSCAMM

    Speaker: Prof. Anna Mazzucato (Mathematics, Penn State University) - http://www.personal.psu.edu/alm24/

    When: Wed, February 21, 2018 - 2:00pm
    Where: CSIC 4122

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    Abstract: I will discuss recent results on the analysis of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations converge to solutions of the Euler equations, for incompressible fluids when walls are present. At small viscosity, a viscous boundary layer arise near the walls where large gradients of velocity and vorticity may form and propagate in the bulk (if the boundary layer separates). A rigorous justification of Prandtl approximation, in absence of analyticity or monotonicity of the data, is available essentially only in the linear or weakly linear regime under no-slip boundary conditions. I will present in particular a detailed analysis of the boundary layer for an Oseen-type equation (linearization around a steady Euler flow) in general smooth domains.
  • Categorification of Young idempotents - Lie Groups and Representation Theory

    Speaker: Matthew Hogancamp (University of Southern California), http://www-bcf.usc.edu/~hogancam/Abstract: I will discuss joint work with Ben Elias in which we construct complexes of Soergel bimodules which categorify the Young idempotents in the Hecke algebras of type A_n. The construction is an application our theory of categorical diagonalization to the case of the full twist Rouqiuer complex acting on Soergel bimodules.  Our categorified Young idempotents are key elements in the Gorsky-Negut-Rasmussen conjectures, which relate categories of Soergel bimodules to Hilbert schemes of points in the plane.  I will explain this connection, and give several examples.

    When: Wed, February 21, 2018 - 2:00pm
    Where: Kirwan 1311

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    Abstract: I will discuss joint work with Ben Elias in which we construct complexes of Soergel bimodules which categorify the Young idempotents in the Hecke algebras of type A_n. The construction is an application our theory of categorical diagonalization to the case of the full twist Rouqiuer complex acting on Soergel bimodules.  Our categorified Young idempotents are key elements in the Gorsky-Negut-Rasmussen conjectures, which relate categories of Soergel bimodules to Hilbert schemes of points in the plane.  I will explain this connection, and give several examples.
  • "Low-rank iterative solvers for stochastic PDEs" and TBA - Student AMSC

    Speaker: Tengfei Su and TBA (AMSC) -

    When: Wed, February 21, 2018 - 3:00pm
    Where: Kirwan Hall 1310
  • Alpha invariants and birational geometry. - Colloquium

    Speaker: Ivan Cheltsov (University of Edinburgh, UK) - http://www.maths.ed.ac.uk/cheltsov/Abstract: Tian introduced alpha invariants to study the existence ofKahler-Einstein metrics on Fano manifolds.In this talk we describe (explicit and implicit) appearance of alphainvariants in (global and local) birational geometry.

    When: Wed, February 21, 2018 - 3:15pm
    Where: Kirwan Hall 3206

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    Abstract: Tian introduced alpha invariants to study the existence ofKahler-Einstein metrics on Fano manifolds.In this talk we describe (explicit and implicit) appearance of alphainvariants in (global and local) birational geometry.
  • Training Quantized Nets: A Deeper Understanding - RIT on Deep Learning

    Speaker: Liam Fowl (UMD) -

    When: Thu, February 22, 2018 - 10:00am
    Where: Kirwan Hall 3206
  • Classical-to-quantum correspondence and transitions in chaotic dynamics of out-of-time-ordered correlators - Applied Dynamics

    Speaker: Victor Galitski - UMD Physics

    When: Thu, February 22, 2018 - 12:30pm
    Where: ERF 1027

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    Abstract: One of the most intriguing phenomena in the studies of classical chaos is the butterfly effect, which manifests itself in that small changes in initial conditions lead to drastically different trajectories. It is characterized by a Lyapunov exponent that measures divergence of the classical trajectories. The question how/if this prototypical effect of classical chaos theory generalizes to quantum systems (where the notion of a trajectory is undefined) has been of interest for decades, but became more popular recently, when it was realized that there exist intriguing connections to string theory and general relativity in some quantum chaotic models. At the center of this activity is the so-called out-of-time-ordered correlator (OTOC) - a quantity that in the classical limit seems to approximate the classical Lyapunov correlator. In this talk, I will discuss the connection between the standard Wigner-Dyson approach to "quantum chaos" and that based on the OTOC on the example of a chaotic billiard and a disordered interacting electron system (i.e., a metal). I will also consider the standard model of quantum and classical chaos - kicked rotor - and calculate the correlator and Lyapunov exponents. The focus will be on how classical chaos and Lyapunov divergence develop in the OTOC and cross-over to the quantum regime. We will see that the quantum out-of-time-ordered correlator exhibits a clear singularity at the Ehrenfest time, when quantum interference effects sharply kick in: transitioning from a time-independent value to its monotonous decrease with time. In conclusion, I will discuss many-body generalizations of such quantum chaotic models.
  • Stochastic properties of the Z^2-periodic Sinai billiard - Dynamics

    Speaker: (Francoise Pene) - http://lmba.math.univ-brest.fr/perso/francoise.pene/

    When: Thu, February 22, 2018 - 2:00pm
    Where: Kirwan Hall 1311

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    Abstract: We study stochastic properties of the Z^2-periodic Sinai billiard (recurrence, ergodicity, mixing, decorrelation, limit theorems).
  • Geometry of parameter space - RIT on Geometry and Physics

    Speaker: Freddy Cisneros -

    When: Thu, February 22, 2018 - 3:30pm
    Where: Physics Bldg 1117

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    Abstract: We'll take a break from generalized complex Kaehler manifolds to discuss geometry of parameter spaces in quantum mechanical models. Reference: notes by Erich Mueller,
    http://muellergroup.lassp.cornell.edu/Basic_Training_Spring_2014/Geometry_files/geometry.pdf
  • Topics in the Nonlinear Schrodinger Equation - Lecture Series (JHU) - Special Lecture

    Speaker: Benjamin Dodson

    When: Fri, February 23, 2018 - 2:00pm
    Where: Room 1313 Kirwan Hall
  • Nonlinear fluid-structure interaction with fiber-reinforced soft composites: a unified mathematical framework for mathematical analysis, computation and applications - Colloquium

    Speaker: Suncica Canic (University of Houston) - https://www.math.uh.edu/~canic/

    When: Fri, February 23, 2018 - 3:15pm
    Where: Kirwan Hall 3206

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    Abstract: Fiber-reinforced structures arise in many engineering and biological applications. Examples include space inflatable habitats, vascular stents supporting compliant vascular walls, and aortic valve leaflets. In all these examples a metallic mesh, or a collection of fibers, is used to support an elastic structure, and the resulting composite structure has novel mechanical characteristics preferred over the characteristics of each individual component. These structures interact with the surrounding deformable medium, e.g., blood flow or air flow, or another elastic structure, constituting a fluid-structure interaction (FSI) problem. Modeling and computer simulation of this class of FSI problems is important for manufacturing and design of novel materials, space habitats, and novel medical constructs.
    Mathematically, these problems give rise to a class of highly nonlinear, moving- boundary problems for systems of partial differential equations of mixed type. To date, there is no general existence theory for solutions of this class of problems, and numerical methodology relies mostly on monolithic/implicit schemes, which suffer from bad condition numbers associated with the fluid and structure sub- problems. In this talk we present a unified mathematical framework to study existence of weak solutions to FSI problems involving incompressible, viscous fluids and elastic structures. The mathematical framework provides a constructive existence proof, and a partitioned, loosely coupled scheme for the numerical solution of this class of FSI problems. The constructive existence proof is based on time-discretization via operator splitting, and on our recent extension of the Aubin-Lions-Simon compactness lemma to problems on moving domains. The resulting numerical scheme has been applied to problems in cardiovascular medicine, showing excellent performance, and providing medically beneficial information. Examples of applications in coronary angioplasty and micro- swimmer biorobot design will be shown.