Upcoming Seminars

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Title: Good and Bad Reduction of Dynatomic Modular Curves
Seminar: Algebra
Speaker: Andrew Obus of University of Virginia
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2017-02-21 at 4:00PM
Venue: W306
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Abstract:
The dynatomic modular curves parameterize one-parameter families of dynamical systems on $P^1$ along with periodic points (or orbits). These are analogous to the standard modular curves parameterizing elliptic curves with torsion points (or subgroups). For the family $x^2 + c$ of quadratic dynamical systems, the corresponding modular curves are smooth in characteristic zero. We give several results about when these curves have good/bad reduction to characteristic $p$, as well as when the reduction is irreducible. These results are motivated by uniform boundedness conjectures in arithmetic dynamics, which will be explained.\\ (This is joint work with John Doyle, Holly Krieger, Rachel Pries, Simon Rubinstein-Salzedo, and Lloyd West.)
Title: Uncertainty Quantification and Numerical Analysis: Interactions and Synergies
Seminar: Numerical Analysis and Scientific Computing
Speaker: Daniela Calvetti of Case Western Reserve University
Contact: James Nagy, nagy@mathcs.emory.edu
Date: 2017-02-24 at 1:00PM
Venue: W301
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Abstract:
The computational costs of uncertainty quantification can be challenging, in particular when the problems are large or real time solutions are needed. Numerical methods appropriately modified can turn into powerful and efficient tools for uncertainty quantification. Conversely, state-of-the-art numerical algorithms reinterpreted from the perspective of uncertainty quantification can becomes much more powerful. This presentation will highlight the natural connections between numerical analysis and uncertainty quantification and illustrate the advantages of re-framing classical numerical analysis in a probabilistic setting.
Title: Optical Design from Art to Car Mirrors
Seminar: N/A
Speaker: Sarah Rody of
Contact: Bree Ettinger, bree.d.ettinger@emory.edu
Date: 2017-02-24 at 3:00PM
Venue: W201
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Abstract:
In order to design a mirror, we must first decide how to write the problem mathematically. I will start by looking at the historical use of perspective and mirrors in art. Then I will discuss how we can trace individual rays of light to describe how a mirror should work. I will show previous examples of optical design such as a non-reversing mirror and a panoramic mirror. Finally, I will turn to the specific example of a car mirror and show one optical design technique that I use. The standard passenger side mirror on a car has a limited field of view which results in a blind spot. Other mirrors, such as spherical mirrors, reduce the blind spot but distort the image. My goal is to find a construction for a passenger side mirror that reduces the blind spot and but creates less distortion than a spherical mirror. The idea central to our construction is the concept of an eigensurface. In general, if a surface is viewed in a curved mirror, it appears distorted. However, there could exist a surface that appears invariant in a particular curved mirror. I will show how I use this idea of eigensurfaces to find a mirror that could work as a passenger side car mirror.
Title: Bounded colorings of graphs and hypergraphs
Seminar: Combinatorics
Speaker: Jan Volec of McGill University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2017-02-27 at 4:00PM
Venue: W303
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Abstract:
A conjecture of Bollobas and Erdos from 1976 states that any coloring of edges of an n-vertex complete graph such that at each vertex no color appears more than (n/2)-times contains a properly-colored Hamilton cycle. This problem was motivation for the following more general question: Let c be a coloring of E(K_n) where at each vertex, no color appear more than k-times. What properly colored subgraphs does c necessarily contain? In this talk, we will be interested in spanning subgraphs of K_n that have bounded maximum degree or the total number of cherries, i.e., the paths on three vertices. We will also mention similar questions for hypergraphs, as well as analogous problems concerned with rainbow subgraphs in edge colorings of K_n, where the total number of appearances for each color is bounded. One of our main results confirms the following conjecture of Shearer from 1979: If G is an n-vertex graph with O(n) cherries and c is a coloring of E(K_n) such that at each vertex every color appears only constantly many times, then c contains a properly colored copy of G. The talk is based on a joint work with Nina Kamcev and Benny Sudakov.
Title: The Distribution Of The Number Of Prime Factors With Restrictions - Variations Of The Classical Theme
Seminar: Algebra
Speaker: Krishna Alladi of University of Florida
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2017-02-28 at 4:00PM
Venue: W306
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Abstract:
The study of $\nu(n)$ the number of prime factors of $n$ began with Hardy and Ramanujan in 1917 who showed that $\nu(n)$ has normal order $log\,log\,n$ regardless of whether the prime factors are counted singly or with multiplicity. Their ingenious proof of this utilized uniform upper bounds for $N_k(x)$, the number of integers up to $x$ with $\nu(n)=k$. Two major results followed a few decades later - the Erd\"os-Kac theorem on the distribution more generally of additive functions, and the Sathe-Selberg theorems on the asymptotic behavior of $N_k(x)$ as $k$ varies with $x$ - a significant improvement of Landau's asymptotic estimate for $N_k(x)$ for fixed $k$. We shall consider the distribution of the number of prime factors by imposing certain restrictions - such as (i) requiring all prime factors of $n$ to be $
Title: TBA
Seminar: Algebra
Speaker: Sujatha Ramdorai of University of British Columbia
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2017-03-21 at 4:00PM
Venue: W306
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Abstract:
TBA
Title: Finite index for arboreal Galois representations
Seminar: Algebra
Speaker: Andrew Bridy of Texas A and M
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2017-03-28 at 4:00PM
Venue: W306
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Abstract:
Let K be a global field of characteristic 0, let f in $K(x)$ and b in K, and set $K_n := K(f^{-n}(b))$. The projective limit of the groups $Gal(K_n/K)$ embeds in the automorphism group of an infinite rooted tree. A difficult problem is to find criteria that guarantee the index is finite; a complete answer would give a dynamical analogue of Serre's famous open image theorem. When f is a cubic polynomial over a function field, I prove a set of necessary and sufficient conditions for finite index (for number fields, the proof is conditional on Vojta's conjecture). This is joint work with Tom Tucker.
Title: Zero-Cycles on Torsors under Linear Algebraic Groups
Defense: Dissertation
Speaker: Reed Sarney of Emory University
Contact: Reed Sarney, reed.sarney@emory.edu
Date: 2017-04-03 at 1:00PM
Venue: W303
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Abstract:
Let $k$ be a field, let $G$ be a smooth connected linear algebraic group over $k$, and let $X$ be a $G$-torsor. Totaro asked: if $X$ admits a zero-cycle of degree $d$, does $X$ have a closed {\'e}tale point of degree dividing $d$? We give a positive answer in two cases: \begin{enumerate} \item $G$ is an algebraic torus of rank $\leq 2$ and $\textup{ch}(k)$ is arbitrary, and \item $G$ is an absolutely simple adjoint group of type $A_1$ or $A_{2n}$ and $\textup{ch}(k) \neq 2$. \end{enumerate} We also present the first known examples where Totaro's question has a negative answer.
Title: Automorphisms of cubic surfaces in arbitrary characteristic
Seminar: Algebra
Speaker: Alexander Duncan of University of South Carolina
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2017-04-04 at 4:00PM
Venue: W306
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Abstract:
TBA
Title: TBA
Seminar: Algebra
Speaker: Cyrus Hettle of Univeristy of Kentucky
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2017-04-18 at 4:00PM
Venue: W306
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Abstract:
TBA