All Seminars
Title: D-optimal Experimental Design for Bayesian Inverse Problems |
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Seminar: Numerical Analysis and Scientific Computing |
Speaker: Dr. Arvind Krishna Saibaba of NC State University |
Contact: Lars Ruthotto, lruthotto@emory.edu |
Date: 2017-10-06 at 2:00PM |
Venue: MSC W301 |
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Abstract: Optimal Experimental Design seeks to control experimental conditions in order to maximize the amount of information gained about parameters of interest, subject to physical or budgetary constraints. The parameters we wish to infer are represented on fine-scale grids; consequently, the experimental design problem is extremely computationally challenging and efficient algorithms are needed. We develop a computational framework for the D-optimality criterion in PDE based inverse problems. Our approach exploits a certain low-rank structure in the covariance matrices using novel randomized estimators. This approach allows us to reduce the computational costs by several orders of magnitude compared to naive approaches. We demonstrate our algorithms on an optimal sensor placement problem from contaminant source identification.\\ \\Joint work with Alen Alexanderian, Ilse CF Ipsen (both at Department of Mathematics, NCSU) |
Title: The rank of the Eisenstein ideal |
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Seminar: Algebra |
Speaker: Preston Wake of UCLA |
Contact: John Duncan, john.duncan@emory.edu |
Date: 2017-10-03 at 4:00PM |
Venue: W306 |
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Abstract: In his landmark 1976 paper "Modular curves and the Eisenstein ideal", Mazur studied congruences modulo p between cusp forms and an Eisenstein series of weight 2 and prime level N. We use deformation theory of pseudorepresentations to study the corresponding Hecke algebra. We will discuss how this method can be used to refine Mazur's results, quantifying the number of Eisenstein congruences. Time permitting, we'll also discuss some partial results in the composite-level case. This is joint work with Carl Wang-Erickson. |
Title: Stabilizing Spectral Functors of Exact Categories |
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Seminar: Algebra |
Speaker: Juan Villeta-Garcia of Emory University |
Contact: John Duncan, john.duncan@emory.edu |
Date: 2017-09-26 at 4:00PM |
Venue: W306 |
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Abstract: Algebraic K-Theory is often thought of as “the” universal additive invariant of rings (or more generally, exact categories). Often, however, functors on exact categories don’t satisfy additivity. We will describe a procedure due to McCarthy that constructs a functor’s universal additive approximation, and apply it to different local coefficient systems, recovering known invariants of rings (K-Theory, THH, etc.). We will talk about what happens when we push these constructions to the world of spectra, and tie in work of Lindenstrauss and McCarthy on the Taylor tower of Algebraic K-Theory. |
Title: Counting restricted orientations of random graphs |
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Seminar: Combinatorics |
Speaker: Yoshi Kohayakawa of University of Sao Paulo |
Contact: Dwight Duffus, dwight@mathcs.emory.edu |
Date: 2017-09-25 at 4:00PM |
Venue: W302 |
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Abstract: Following a suggestion of Erdos (1974), Alon and Yuster (2006) investigated the maximum number of orientations graphs of a given order admit if we forbid copies of a fixed tournament. We discuss the analogous problem in which certain restricted orientations of typical graphs of a given order and a given number of edges are considered.\\ \\This is joint work with M. Collares (Belo Horizonte), R. Morris (Rio de Janeiro) and G. O. Mota (Sao Paulo). |
Title: A new tensor framework - theory and applications |
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Seminar: Numerical Analysis and Scientific Computing |
Speaker: Dr. Misha Kilmer of Tufts University |
Contact: James Nagy, jnagy@emory.edu |
Date: 2017-09-22 at 2:00PM |
Venue: MSC W301 |
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Abstract: Tensors (aka multiway arrays) can be instrumental in revealing latent correlations residing in high dimensional spaces. Despite their applicability to a broad range of applications in machine learning, speech recognition, and imaging, inconsistencies between tensor and matrix algebra have been complicating their broader utility. Researchers seeking to overcome those discrepancies have introduced several different candidate extensions, each introducing unique advantages and challenges. In this talk, we review some of the common tensor definitions, discuss their limitations, and introduce our tensor product framework which permits the elegant extension of linear algebraic concepts and algorithms to tensors. Following introduction of fundamental tensor operations, we discuss in further depth tensor decompositions and in particular the tensor SVD (t-SVD) and its randomized variant, which can be computed efficiently in parallel. We present details of the t-SVD, theoretical results, and provide numerical results that show the promise of our approach for compression and analysis of operators and datasets, highlighting examples such as facial recognition and model reduction. |
Title: Unifying relaxed notions of modular forms |
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Seminar: Algebra |
Speaker: Martin Raum of Chalmers Technical University, Gothenburg, Sweden |
Contact: John Duncan, john.duncan@emory.edu |
Date: 2017-09-21 at 4:00PM |
Venue: W306 |
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Abstract: Elliptic modular forms are functions on the complex upper half plane that are invariant under a certain action of the special linear group with integer entries. Their history comprises close to two centuries of amazing discoveries and application: The proof of Fermat's Last Theorem is probably the most famous; The theory of theta functions is among its most frequently employed parts.\\ \\During the past decade it has been à la mode to study relaxed notions of modularity. Relevant keywords that we will discuss are mock modular forms and higher order modular forms. We have witnessed their application, equally stunning as surprising, to conformal field theory, string theory, combinatorics, and many more areas.\\ \\In this talk, we suggest a change of perspective on such generalizations. Most of the novel variants of modular forms (with one prominent exception) can be viewed as components of vector-valued modular forms. This unification draws its charm from the past and the future. On the one hand, we integrate results by Kuga and Shimura that hitherto seemed almost forgotten. On the other hand, we can point out connections, for example, between mock modular forms and so-called iterated integrals that have not yet been noticed. Experts will be pleased to have in the future a ``Petersson pairing'' for mixed mock modular forms at their disposal.\\ \\This is joint work with Michael Mertens |
Title: On the Birkhoff--von Neumann decomposition and its use in solving sparse linear systems |
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Seminar: Numerical Analysis and Scientific Computing |
Speaker: Dr. Bora Ucar of CNRS and ENS Lyon, France (visiting GaTech this year) |
Contact: Michele Benzi, benzi@mathcs.emory.edu |
Date: 2017-09-15 at 2:00PM |
Venue: MSC W301 |
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Abstract: The Birkhoff--von Neumann decomposition expresses a doubly stochastic matrix as a convex combination of permutation matrices. This talk will be an introduction to this decomposition. We are going to see its use in solving sparse linear systems, and investigate some algorithmic and combinatorial problems associated with it. This talk contains results from joint work with Michele Benzi (Emory Univ., Atlanta), Fanny Dufosse (Inria, France), Kamer Kaya (Sabanci Univ, Turkey), and Ioannis Panagiotas (ENS Lyon, France). |
Title: Linked Fields of Characteristic 2 and their u-Invariant. |
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Seminar: Algebra |
Speaker: Dr. Adam Chapman of Tel-Hai Academic College, Israel. |
Contact: Dr. John Duncan, john.duncan@emory.edu |
Date: 2017-09-14 at 4:00PM |
Venue: W306 |
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Abstract: The u-invariant of a field is the maximal dimension of a nonsingular anisotropic quadratic form over that field, whose order in the Witt group of the field is finite. By a classical theorem of Elman and Lam, the u-invariant of a linked field of characteristic different from 2 can be either 0,1,2,4 or 8. The analogous question in the case of characteristic 2 remained open for a long time.. We will discuss the proof of the equivalent statement in characteristic 2, recently obtained in a joint work by Andrew Dolphin and the speaker. |
Title: Spectrum of singularities, exponential sums and the irreducibility of polynomials in two variables |
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Seminar: Algebra |
Speaker: Jorge Jimenez Urroz of U. Politecnica, Catalunya |
Contact: John Duncan, john.duncan@emory.edu |
Date: 2017-08-29 at 4:00PM |
Venue: W306 |
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Abstract: In order to control the spectrum of singularities of the generalized Riemann function, we need to find sharp bounds for certain kind of Gauss sums with frequencies on polynomials. This can be achieved by Weil bounds on completely irreducible algebraic curves, which lead us to prove some theorems on irreducibility of polynomials in two variables. We will prove a general theorem in this field. An example of the theorem is the absolute irreducibility of p(x)-p(y)+1, for any p(x) with integer coefficients. |
Title: Topics in Tropical and Analytic Geometry |
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Defense: Dissertation |
Speaker: Charles Morrissey of Emory University |
Contact: Charles Morrissey, cjmorr3@emory.edu |
Date: 2017-08-10 at 2:00PM |
Venue: W306 |
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Abstract: In this thesis, the author proves theorems on the existence and mapping properties of tropical stacks that arise from result concerning toric Artin stacks. The author also provides a generalization, using the same ideas from the toric Artin stacks, of recent work involving analytic stacks and their tropicalizations. The author also proves results on the notion of a tropical jet space. |