All Seminars
| Title: Existence and uniqueness of Green's function to a nonlinear Yamabe problem |
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| Colloquium: Analysis and Differential Geometry |
| Speaker: Yanyan Li of Rutgers University |
| Contact: Vladimir Oliker, oliker@emory.edu |
| Date: 2018-10-18 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: For a given finite subset S of a compact Riemannian manifold (M; g) whose Schouten curvature tensor belongs to a given cone, we establish a necessary and sufficient condition for the existence and uniqueness of a conformal metric on M minus S such that each point of S corresponds to an asymptotically flat end and that the Schouten tensor of the new conformal metric belongs to the boundary of the given cone. This is a joint work with Luc Nguyen. |
| Title: On a Question of Gross and McMullen |
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| Seminar: Algebra |
| Speaker: Eva Bayer Fluckinger of EPFL |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2018-10-16 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: In a joint work with Lenny Taelman, we characterize the irreducible polynomials that occur as a characteristic polynomial of an isometry of an even, unimodular lattice with given signature, answering a question of Gross and McMullen. It turns out that the criteria are local ones, and that in the case of an irreducible polynomial, one has a local-global principle. This is no longer true for reducible polynomials. The aim of the talk is to describe these results, and give to a criterion for the local-global principle to hold. |
| Title: Energy and equilibrium for granular materials |
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| Seminar: Analysis and Differential Geometry |
| Speaker: John McCuan of Georgia Institute of Technology |
| Contact: Vladimir Oliker, oliker@emory.edu |
| Date: 2018-10-16 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: We consider a model for multi-grain clusters of material on a substrate involving scaled surface energies. It is shown that natural equilibrium conditions are not sufficient to ensure an energy equilibrium in certain cases. Theoretical and numerical results suggest the possibility of a gravity driven granular scale. This is joint work with Vadim Derdach, Amy Novick-Cohen, and Ray Treinen. |
| Title: Inductive Methods for Counting Number Fields |
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| Seminar: Algebra |
| Speaker: Jiuya Wang of Duke University |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2018-10-02 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: We propose general frameworks to inductively counting number fields. By applying these methods, we prove the asymptotic distribution for extensions with Galois groups in the form of direct product or wreath product. For both way of inductions, the key ingredients are uniform estimates on the number of number fields with certain conditions. By unifying the approaches, we extend the framework to a more general set up and prove results for more general type of products. This will involve my thesis and in progress work with Robert J. Lemke Oliver and Melanie Matchett Wood. |
| Title: On the Erdos-Gyarfas distinct distances problem with local constraints |
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| Seminar: Combinatorics |
| Speaker: Cosmin Pohoata of The California Institute of Technology |
| Contact: Dwight Duffus, dwightduffus@emory.edu |
| Date: 2018-10-01 at 4:00PM |
| Venue: MSC E408 |
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| Abstract: In 1946 Erdos asked to determine or estimate the minimum number of distinct distances determined by an n-element planar point set V. He showed that a square integer lattice determines \Theta(n/\sqrt{log n}) distinct distances, and conjectured that any n-element point set determines at least n^{1−o(1)} distinct distances. In 2010-2015, Guth and Katz answered Erdos’s question by proving that any n-element planar point set determines at least \Omega(n/log n) distinct distances. In this talk, we consider a variant of this problem by Erdos and Gyarfas. For integers n, p, q with p \geq q \geq 2, determine the minimum number D(n,p,q) of distinct distances determined by a planar n-element point set V with the property that any p points from V determine at least q distinct distance. In a recent paper, Fox, Pach and Suk prove that when q = {p \choose 2} - p + 6, D(n,p,q) is always at least n^{8/7 - o(1)}. We will discuss a recent improvement of their result and some new bounds for a related (graph theoretic) Ramsey problem of Erdos and Shelah which arise. This is joint work with Adam Sheffer. |
| Title: Local-to-Global Extensions for Wildly Ramified Covers of Curves |
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| Seminar: Algebra |
| Speaker: Renee Bell of University of Pennsylvania |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2018-09-25 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: Given a Galois cover of curves $X \to Y$ with Galois group $G$ which is totally ramified at a point $x$ and unramified elsewhere, restriction to the punctured formal neighborhood of $x$ induces a Galois extension of Laurent series rings $k((u))/k((t))$. If we fix a base curve $Y$, we can ask when a Galois extension of Laurent series rings comes from a global cover of $Y$ in this way. Harbater proved that over a separably closed field, every Laurent series extension comes from a global cover for any base curve if $G$ is a $p$-group, and he gave a condition for the uniqueness of such an extension. Using a generalization of Artin--Schreier theory to non-abelian $p$-groups, we characterize the curves $Y$ for which this extension property holds and for which it is unique up to isomorphism, but over a more general ground field. |
| Title: Signed tropicalization of semialgebraic sets |
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| Seminar: Algebra |
| Speaker: Philipp Jell of Georgia Tech |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2018-09-18 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: Tropicalzation of algebraic varieties has been proven to be a powerful tool in complex, real and arithmetic geometry. Different methods to tropicalize are shown to be equivalent by the tropical fundamental theorem. I will explain this theorem and report on joint work in progress with Claus Scheiderer and Josephine Yu. In this work we generalize the fundamental theorem to so call "signed tropicalizations" of semialgebraic sets and define the signed non-archimedean analytification of a semialgebraic set. |
| Title: Moonshine for Finite Groups |
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| Seminar: Algebra |
| Speaker: Madeline Locus Dawsey of Emory University |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2018-09-11 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: {\it Weak moonshine} for a finite group $G$ is the phenomenon where an infinite dimensional graded $G$-module $$V_G=\bigoplus_{n\gg-\infty}V_G(n)$$ has the property that its trace functions, known as McKay-Thompson series, are modular functions. Recent work by Dehority, Gonzalez, Vafa, and Van Peski established that weak moonshine holds for every finite group. Since weak moonshine only relies on character tables, which are not isomorphism class invariants, non-isomorphic groups can have the same McKay-Thompson series. We address this problem by extending weak moonshine to arbitrary width $s\in\mathbb{Z}^+$. For each $1\leq r\leq s$ and each irreducible character $\chi_i$, we employ Frobenius' $r$-character extension $\chi_i^{(r)} \colon G^{(r)}\rightarrow\mathbb{C}$ to define McKay-Thompson series of $V_G^{(r)}:=V_G\times\cdots\times V_G$ ($r$ copies) for each $r$-tuple in $G^{(r)}:=G\times\cdots\times G$ ($r$ copies). These series are modular functions. We find that {\it complete} width 3 weak moonshine always determines a group up to isomorphism. Furthermore, we establish orthogonality relations for the Frobenius $r$-characters, which dictate the compatibility of the extension of weak moonshine for $V_G$ to width $s$ weak moonshine. |
| Title: Research Spotlights |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Alessandro Veneziani and Yuanzhe Xi of Emory University |
| Contact: Lars Ruthotto, lruthotto@emory.edul |
| Date: 2018-09-07 at 2:00PM |
| Venue: MSC N302 |
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| Abstract: The scientific computing group at Emory welcomes all for the second round of research spotlights. This week, Dr. Veneziani and Dr. Xi will present their groups’ work. Dr. Veneziani will give an overview of his work on numerical partial differential equations and their impact on medical decision-making. Dr. Xi will present new and ongoing work in high-performance computing for numerical linear algebra with applications in physics and machine learning. These high-level talks will not be too technical, and faculty and students working in other but related fields are encouraged to attend. |
| Title: Research Spotlights |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: James Nagy and Lars Ruthotto of Emory University |
| Contact: Lars Ruthotto, lruthotto@emory.edu |
| Date: 2018-08-31 at 2:00PM |
| Venue: MSC N302 |
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| Abstract: The scientific computing group at Emory will kick off the new academic year by short overviews of the faculty's ongoing research. This week, Dr. Nagy and Dr. Ruthotto will be in the spotlight. Dr. Nagy will give his overview of his group's efforts aiming at developing more efficient numerical linear algebra techniques for large-scale image processing. Dr. Ruthotto will present recent advances and open problems at the interface between PDEs, optimization, and machine learning. These high-level talks will not be too technical and faculty and students working in other but related fields are encouraged to attend. |