All Seminars

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Title: An upper bound on the size of a $k$-uniform family with covering number $k$
Seminar: Combinatorics
Speaker: John Retter of Emory University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2016-04-18 at 4:00PM
Venue: W301
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Abstract:
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Title: Topics in Decision Analysis for Cloud Computing
Seminar: Computer Science
Speaker: Radhika Garg of University of Zurich, Zurich, Switzerland
Contact: Avani Wildani, avani@mathcs.emory.edu
Date: 2016-04-15 at 3:00PM
Venue: W301
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Abstract:
Adopting a new technology in an organization is a crucial decision as its impact can be at technical, economical, and organizational level. One of such decisions is related to adoption of Cloud-based services in an organization. Cloud Computing is changing the way IT infrastructure is used today primarily due to high cost savings associated to it. However, if the solution adopted by an organization is not fulfilling its requirements, it can have tremendous negative consequences at technical, economical, and organizational level. Therefore, the decision to adopt Cloud-based services should be based on a methodology that supports a wide array of criteria for evaluating any available alternative. Also, as these criteria or factors can be mutually interdependent and conflicting, a trade-offs- based methodology is needed to make such decisions. In addition, inclusion and modeling of qualitative factors (e.g., legal and regulative constraints) that influence such a decision forms a crucial part of this methodology. This talk, therefore, discusses the design and implementation of Trade-offs based Methodology for Adoption of Cloud-based Services (TrAdeCIS). This methodology is based on Multi-attribute Decision Algorithms (MADA), which selects the best alternative, based on the priorities given to different criteria by decision maker. Furthermore, the talk will be concluded with the extendibility and applicability of this methodology to other domains.
Title: Athens-Atlanta Joint Number Theory Seminar
Type: Number Theory
Speaker: Hosted by Georgia Tech of
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2016-04-14 at 4:00PM
Venue: Skiles 006
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Abstract:
The speakers are Melanie Matchett-Wood (UW-Madison) Zhiwei Yun (Stanford)
Title: Zeta polynomials for modular form periods
Seminar: Algebra
Speaker: Ken Ono of Emory University
Contact: David Zurieck-Brown, dzb@mathcs.emory.edu
Date: 2016-04-12 at 4:00PM
Venue: W304
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Abstract:
Yuri Manin has been developing a theory of zeta-polynomials, polynomials which are arithmetic geometric in origin which also satisfy a functional equation and the Riemann Hypothesis. He conjectured the existence of such functions for all newforms which arise from critical values of L-functions. We confirm his conjecture by constructing a Bloch-Kato complex using weighted moments of orders of Tate-Shafarevich groups. Surprisngly, for fixed weights, as levels tend to infinity we find these zeta-polynomials converge to Earhart polynomials for classical polytopes. This is joint work with Larry Rolen and Florian Sprung.
Title: Log Canonical ring of a graph curve
Masters thesis defense: Algebra
Speaker: William Baker of Emory University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2016-04-11 at 4:00PM
Venue: E408
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Abstract:
TBA
Title: Topics in Elliptic Curves
Defense: Masters Thesis
Speaker: Jackson Morrow of Emory University
Contact: Jackson Morrow, jmorro2@emory.edu
Date: 2016-04-05 at 4:00PM
Venue: W304
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Abstract:
In this thesis, the author proves theorems relating to three different areas in the study of elliptic curves: torsion subgroups over number fields, Selmer groups of elliptic curves, and composite level images of Galois. In particular, the thesis contains theorems completing the classification of possible torsion subgroups for elliptic curves defined over cubic number fields; bounding the order of l-Selmer groups for twists of elliptic curves defined over number fields of small degree; and determining the possibilities, indicies, and occurrences of composite level images of Galois for elliptic curves defined over Q.
Title: Clifford algebras and the search for Ulrich bundles
Seminar: Algebra
Speaker: Danny Krashen of University of Georgia
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2016-04-04 at 4:00PM
Venue: W301
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Abstract:
The classical notion of the Clifford algebra of a quadratic form has been generalized to other types of higher degree forms by a number of authors. The representations of these generalized Clifford algebras turn out to correspond to “Ulrich bundles,” which are a very special class of vector bundle on a hypersurface. In this talk, I’ll describe joint work with Adam Chapman and Max Lieblich of a new construction, generalizing the previous ones, of a Clifford algebra of a finite morphism of proper schemes, I’ll discuss connections to the arithmetic of genus 1 curves, and I’ll present some new results on the existence of Ulrich bundles.
Title: R-equivalence and norm principles in algebraic groups
Defense: Dissertation
Speaker: Nivedita Bhaskhar of Emory University
Contact: Nivedita Bhaskhar, nbhaskh@emory.edu
Date: 2016-03-31 at 2:30PM
Venue: W304
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Abstract:
We start by exploring the theme of R-equivalence in algebraic groups. First introduced by Manin to study cubic surfaces, this notion proves to be a fundamental tool in the study of rationality of algebraic group varieties. A k-variety is said to be rational if its function field is purely transcendental over k. We exploit Merkurjev's fundamental computations of R-equivalence classes of adjoint classical groups and give a recursive construction to produce an infinite family of non-rational adjoint groups coming from quadratic forms. In a different direction, we address Serre's injectivity question which asks whether a principal homogeneous space under a linear algebraic group admitting a zero cycle of degree one in fact has a rational point. We give a positive answer to this question for any smooth connected reductive k-group whose Dynkin diagram contains connected components only of type A_n, B_n or C_n by relating Serre's question to the norm principles previously proved by Barquero and Merkurjev. The study of norm principles are interesting in their own right and we examine in detail the case of groups of type (non-trialitarian) D_n and get a scalar obstruction defined up to spinor norms whose vanishing will imply the norm principle for them. This in turn will also yield a positive answer to Serre's question for all connected reductive k-groups of classical type.
Title: Metabelian Galois Representations
Colloquium: Algebra
Speaker: Edray H. Goins of Purdue
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2016-03-31 at 4:00PM
Venue: W306
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Abstract:
We are used to working with Galois representations associated to elliptic curves by considering the action of the absolute Galois group on torsion points. However there is a slightly more exotic way to view this construction once we realize that the Tate module of an elliptic curve is just the abelianization of the etale fundamental group of the punctured torus. In this talk, we discuss how to construct a class of Galois representations by considering covers of elliptic curves which are branched over one point. We discuss how this is related to the question of surjectivity of certain Galois representation, and how to construct representations with image isomorphic to the holomorph of the quaternions. We will not assume extensive knowledge of etale cohomology. This is joint work with Rachel Davis.
Title: Topics in Analytic Number Theory
Defense: Dissertation
Speaker: Jesse Thorner of Emory University
Contact: Ken Ono, ono@mathcs.emory.edu
Date: 2016-03-31 at 5:15PM
Venue: W306
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Abstract:
In this thesis, the author proves theorems on the distribution of primes by extending recent results in sieve theory and proving new results on the distribution of zeros of Rankin-Selberg L-functions. The author proves for any Galois extension of number fields K/Q, there exist bounded gaps between primes with a given ``splitting condition'' in K, and the primes in question may be restricted to short intervals. Furthermore, we can count these gaps with the correct order of magnitude. This follows from proving a short interval variant of the Bombieri-Vinogradov theorem in a Chebotarev setting and generalizing the recent progress in sieve theory due to Maynard and Tao. The author also proves several log-free zero density estimates for Rankin-Selberg L-functions with effective dependence on the key parameters. From this, the author proves an approximation of the short interval prime number theorem for Rankin-Selberg L-functions, an approximation of the short interval version of the Sato-Tate conjecture, and a bound on the least norm of a prime ideal counted by the Sato-Tate conjecture. All of these results exhibit effective dependence on the key parameters.