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  • A numerical invariant for representations of algebras - Algebra-Number Theory

    Speaker: Zinovy Reichstein (University of British Columbia) -

    When: Mon, April 23, 2018 - 2:00pm
    Where: Kirwan Hall 3206

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    Abstract: A classical theorem of Brauer asserts that every finite-dimensional
    non-modular representation ρ of a finite group G defined over a
    field K, whose character takes values in a subfield k, descends to k,
    provided that k has suitable roots of unity. If k does not contain
    these roots of unity, it is natural to ask how far ρ is from being
    definable over k. The classical answer is given by the Schur index of
    ρ, which is the smallest degree of a finite field extension l/k
    such that ρ can be defined over l. In this talk, based on joint
    work with Nikita Karpenko, Julia Pevtsova and Dave Benson, I will
    discuss another invariant, the essential dimension of ρ. This
    invariant measures "how far" ρ is from being definable over k in a
    different way, by using transcendental, rather than algebraic field
    extensions. I will also discuss related work on representations of
    algebras, due to Federico Scavia.
  • Phase retrieval in infinite dimensional Hilbert spaces - RIT on Applied Harmonic Analysis

    Speaker: Michael Rawson (UMD) -

    When: Mon, April 23, 2018 - 3:00pm
    Where: Kirwan Hall 1308
  • Stability of 3D Couette Flow - RIT on Applied PDE

    Speaker: Kyle Liss (University of Maryland) -

    When: Mon, April 23, 2018 - 3:00pm
    Where: Kirwan Hall 1311

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  • Point games and Coin Flipping protocols - RIT on Quantum Information

    Speaker: Aarthi Sundaram (University of Maryland) -

    When: Mon, April 23, 2018 - 4:15pm
    Where: Atlantic 3100A

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    Abstract: Kitaev's point game formalism was used by Mochon (arXiv:0711.4114) to show the existence of a quantum weak coin flipping protocol with arbitrarily small bias and is a fundamental result in quantum cryptography. Though this result has been used as a black-box in a number of other follow-up results, the novel techniques used in this proof (especially Kitaev's point game formalism) are not well understood. It is believed that a complete grasp of these techiniques could shed more light on the role of entanglement in quantum protocols as well as find other applications where point games can be used. One direction to find this understanding may lie in finding a graphical calculus representation for point games. As a first step in that direction, I will discuss our current grasp of this formalism based on the work done by Aharanov et al. (arXiv:1402.7166) to simplify and clarify some parts of Mochon's original proof.
  • Large Deviation Principles for Dynamical Systems - Student Dynamics

    Speaker: Kasun Fernando (UMD) -

    When: Tue, April 24, 2018 - 3:15pm
    Where: Kirwan Hall 1310
  • Generalizing Tree Decomposition - Logic

    Speaker: Miriam Parnes (Wesleyan University) -

    When: Tue, April 24, 2018 - 3:30pm
    Where: Kirwan Hall 1311

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    Abstract: Questions which are hard to answer about a graph often become easy if we know a bound for the graph's tree width. The tree width of a graph, which tells us how tree-like the graph is, comes from its tree decompositions. In this talk, we will explore extensions of the concepts of tree decomposition and tree width to the more general setting of algebraically trivial Fraïssé classes on which a particular kind of independence relation is defined.
  • Rate optimal adaptivity and LU-factorization - Numerical Analysis

    Speaker: Michael Feischl (KIT Karlsruhe) -

    When: Tue, April 24, 2018 - 3:30pm
    Where: Kirwan Hall 3206

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    Abstract: We develop a framework which allows us to prove the essential general quasi-orthogonality for non-symmetric and indefinite problems as the stationary Stokes problem or certain transmission problems. General quasi-orthogonality is a necessary ingredient of rate optimality proofs and is the major difficulty on the way to prove rate optimal convergence of adaptive algorithms for many strongly non-symmetric or indefinite problems. The proof exploits a new connection between the general quasi-orthogonality and LU-factorization of infinite matrices.
  • Moduli spaces of dilation surfaces - Student Geometry and Topology

    Speaker: Jenny Rustad (UMD) -

    When: Wed, April 25, 2018 - 1:00pm
    Where: Kirwan Hall 1310
  • Signal Fragmentation for Low Frequency Radio Transmission - CSCAMM

    Speaker: Russel E. Caflisch (Director and Professor of Mathematics, Courant Institute of Mathematical Sciences at New York University) -

    When: Wed, April 25, 2018 - 2:00pm
    Where: CSIC 4122

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    Abstract: Signal fragmentation is a method for transmitting a low frequency signal over a collection of small antennas through a modal expansion (similar to one level of a wavelet expansion), in which the mode has compact support in time. We analyze the spectral leakage and optimality of signal fragmentation. For a special choice of mode, the spectral leakage can be eliminated for sinusoidal signals and minimized for bandlimited or AM signals. We derive the optimal mode for either support size or for energy efficiency. The derivation of these results uses the Poisson summation formula and the Shannon Interpolation Formula.
  • TBA - Colloquium

    Speaker: Alexander Vladimirsky (Cornell University) -

    When: Wed, April 25, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • High-speed prediction of a chaotic system using reservoir computers - Applied Dynamics

    Speaker: Dan Gauthier - Ohio State Department of Physics

    When: Thu, April 26, 2018 - 12:30pm
    Where: ERF 1027

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    Abstract: A reservoir computer is an approach to machine learning that appears to be ideally suited for classifying time varying signals or as a black-box system for forecasting the behavior of a dynamical system. It consists of a recurrent artificial neural network that serves as a “universal” dynamical system into which data are input, where the connections on the input layer and recurrent links within the network are chosen randomly and held fixed. Only the weights of network output layer are adjusted during the training period, which greatly reduces the training time. I will discuss our recent progress on realizing high-speed prediction of the Mackey-Glass chaotic system (>10^8 predictions per second) using a reservoir computer based on a time-delay autonomous Boolean network realized on a field programmable gate array. I will also touch on our efforts to control a dynamical system with a reservoir computer and some recent results on methods to identify the optimum size of the reservoir computer network for a given task.
  • Recent results in diffraction theory - Dynamics

    Speaker: E. Arthur Robinson (George Washington University) -

    When: Thu, April 26, 2018 - 2:00pm
    Where: Kirwan Hall 1311

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    Abstract: A quasicrystal is, by one definition, a solid with non-classical diffraction pattern, e.g, 5-fold rotational symmetry. The first quasicrystal was discovered by D. Schectman at NIST in around 1984, for which he ultimately won the 2011 Chemistry Nobel prize. At the time, several physicists suggested the vertex set of a Penrose tiling (or its 3-dimensional analogue) as a model for the placement of atoms in a quasicrystal. The diffraction theory of vertex sets of Penrose-like tilings is closely tied to the dynamical spectrum (especially the point spectrum) of a corresponding type of dynamical system. In this talk, we will start with an overview of this type of dynamical system and the corresponding diffraction theory. Then we will describe some recent new results in this area, most of which concern the spectral and mixing properties of different types of substitution dynamical systems.
  • Categorical Mirror symmetry of elliptic curves - RIT on Geometry and Physics

    Speaker: Matt Kukla --

    When: Thu, April 26, 2018 - 3:30pm
    Where: Physics Bldg 1117

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    Abstract: See also
  • Counting points, counting fields, and new heights - Colloquium

    Speaker: Jordan Ellenberg

    When: Fri, April 27, 2018 - 11:00am
    Where: Kirwan Hall 3206

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    Abstract: The basic objects of algebraic number theory are number fields, and the basic invariant of a number field is its discriminant, which in some sense measures its arithmetic complexity. A basic finiteness result, proved by Hermite at the end of the 19th century, is that there are only finitely many degree-d number fields of discriminant at most X. It thus makes sense to put all the number fields in order of their discriminant, and ask if we can say how many you’ve encountered by the time you get to discriminant X.

    This is an old problem, governed by a conjecture of Narkiewicz. Interest in this area was revitalized by the work of Bhargava; the first step in his program was to count number fields of degree 4 and 5. (Degree 6 remains completely out of reach!) I’ll talk about the long history of this problem and its variants, and discuss two recent results:

    1) (joint with TriThang Tran and Craig Westerland) We prove that the upper bound conjectured by Narkiewicz is true “up to epsilon" when Q is replaced by a rational function field F_q(t) — this is much more than is known in the number field case, and relies on a new upper bound for the cohomology of Hurwitz spaces coming from quantum shuffle algebras:

    2) (joint with Matt Satriano and David Zureick-Brown) Another much-studied counting problem in number theory is the Batyrev-Manin conjecture, which asks about the number of rational points on a variety of bounded height, or, in more concrete terms, questions like:
    “How many solutions does an equation like x^3 + y^3 + z^3 + w^3 = 0 have in integers of absolute value at most X?”

    It turns out there’s a way to synthesize the Narkiewicz conjecture and the Batyrev-Manin conjecture into a unified heuristic which includes both of those conjectures as special cases, and which says much more in general. This involves defining “the height of a rational point on an algebraic stack” and I will say as much about what this means as there’s time to!
  • The Geometry of Redistricting - Jordan Ellenberg - Colloquium

    When: Fri, April 27, 2018 - 3:30pm
    Where: 3206 Kirwan Hall