Upcoming Seminars

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Title: Compositional Models for Information Extraction
Seminar: N/A
Speaker: Mark Dredze of Johns Hopkins University
Contact: Eugene Agichtein, eugene@mathcs.emory.edu
Date: 2017-03-27 at 4:00PM
Venue: White Hall 207
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Abstract:
Information extraction systems are the backbone of many end-user applications, including question answering, web search and clinical text analysis. These applications depend on underlying technologies that can identify entities and relations as expressed in natural language text. For example, Amazon Echo may answer a user question based on a relation extracted from a news article. A clinical decision support system may offer a physician suggestions based on a symptom identified in the clinical notes from a previous patient visit. In political science, we may seek to aggregate opinions expressed in public comments about a new public policy. Advances in machine learning have led to new neural models for learning effective representations directly from data that improve information extraction tasks. Yet for many tasks, years of research have created hand-engineered features that yield state of the art performance. I will present feature-rich compositional models that combine both hand-engineered features with learned text representations to achieve new state-of-the-art results for relation extraction. These models are widely applicable to problems within natural language processing and beyond. Additionally, I will survey how these models fit into my broader research program by highlighting work by my group on developing new machine learning methods for extracting public health information from clinical and social media text.
Title: On Saturation Spectrum
Defense: Dissertation
Speaker: Jessica Fuller of Emory
Contact: Jessica Fuller, jfulle@emory.edu
Date: 2017-03-28 at 2:45PM
Venue: E406
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Abstract:
Given a graph H, we say a graph G is H-saturated if G does not contain H as a subgraph and the addition of any edge not already in G results in H as a subgraph. The question of the minimum number of edges of an H saturated graph on n vertices, known as the saturation number, and the question of the maximum number of edges possible of an H -saturated graph, known as the Turᮠnumber, has been addressed for many different types of graphs. We are interested in the existence of H -saturated graphs for each edge count between the saturation number and the Turᮠnumber. We determine the saturation spectrum of (Kt-e)-saturated graphs and Ft-saturated graphs. Let (Kt-e) be the complete graph minus one edge. We prove that (Kt-e)-saturated graphs do not exist for small edge counts and construct (Kt-e)-saturated graphs with edge counts in a continuous interval. We then extend the constructed (Kt-e)-saturated graphs to create (Kt-e)-saturated graphs. Let Ft be the graph consisting of t edge-disjoint triangles that intersect at a single vertex v. We prove that F2-saturated graphs do not exist for small edge counts and construct a collection of F2-saturated graphs with edge counts in a continuous interval. We also establish more general constructions that yield a collection of Ft-saturated graphs with edge counts in a continuous interval.
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: A Study of Benford's Law for the Values of Arithmetic Functions
Defense: Honors
Speaker: Letian Wang of Emory University
Contact: Letian Wang, letian.wang@emory.edu
Date: 2017-03-29 at 1:00PM
Venue: E408
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Abstract:
"Benford's Law characterizes the distribution of initial digits in large datasets across disciplines. Since its discovery by Simon Newcomb in 1881, Benford's Law has triggered tremendous studies. In this paper, we will start by introducing the history of Benford's Law and discussing in detail the explanations proposed by mathematicians on why various datasets are Benford. Such explanations include the Spread Hypothesis, the Geometric, the Scale-Invariance, and the Central Limit explanations. "To rigorously de ne Benford's Law and to motivate criteria for Benford sequences, we will provide fundamental theorems in uniform distribution modulo 1 in Chapter 2. We will state and prove criteria for checking uniform distribution, including Weyl's Criterion, Van der Corput's Di erence Theorem, as well as their corollaries.\\ \\"In Chapter 3, we will introduce the logarithm map, which allows us to reformulate Benford's Law with uniform distribution modulo 1 studied earlier. We will start by examining the case of base 10 only and then generalize to arbitrary bases. "Finally, we will elaborate on the idea of good functions. We will prove that good functions are Benford, which in turn enables us to nd a new class of Benford sequences. We will use this theorem to show that the partition function p(n) and the factorial sequence n! follow Benford's Law."
Title: Scalable Computational pathology: From Interactive to Deep Learning
Defense: Dissertation
Speaker: Michael Nalisnik of Emory University
Contact: Lee Cooper, lee.cooper@emory.edu
Date: 2017-03-30 at 10:00AM
Venue: W306
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Abstract:
Advances in microscopy imaging and genomics have created an explosion of patient data in the pathology domain. Whole-slide images of histologic sections contain rich information describing the diverse cellular elements of tissue microenvironments. These images capture, in high resolution, the visual cues that have been the basis of pathologic diagnosis for over a century. Each whole-slide image contains billions of pixels and up to a million or more microanatomic objects whose appearances hold important prognostic information. Combining this information with genomic and clinical data provides insight into disease biology and patient outcomes. Yet, due to the size and complexity of the data, the software tools needed to allow scientists and clinicians to extract insight from these resources are non-existent or limited. Additionally, current methods utilizing humans is highly subjective and not repeatable. This work aims to address these shortcomings with a set of open-source computational pathology tools which aim to provide scalable, objective and repeatable classification of histologic entities such as cell nuclei.\\ \\ We first present a comprehensive interactive machine learning framework for assembling training sets for the classification of histologic objects within whole-slide images. The system provides a complete infrastructure capable of managing the terabytes worth of images, object features, annotations and metadata in real-time. Active learning algorithms are employed to allow the user and system to work together in an intuitive manner, allowing the efficient selection of samples from unlabeled pools of objects numbering in the hundreds of millions. We demonstrate how the system can be used to phenotype microvascular structures in gliomas to predict survival, and to explore the molecular pathways associated with these phenotypes. Quantitative metrics are developed to describe these structures.\\ \\ We also present a scalable, high-throughput, deep convolutional learning framework for the classification of histologic objects is presented. Due to its use of representation learning, the framework does not require the images to be segmented, instead learning optimal task-specific features in an unbiased manner. Addressing scalability, the graph-based, parallel architecture of the framework allows for the processing of large whole-slide image archives consisting of hundreds of slides and hundreds of millions of histologic objects. We explore the efficacy of various deep convolutional network architectures and demonstrate the system's capabilities classifying cell nuclei in lower grade gliomas.
Title: The Artin-Schreier Theorem in Galois Theory
Defense: Honors Thesis
Speaker: Yining Cheng of Emory University
Contact: TBA
Date: 2017-03-30 at 1:00PM
Venue: W303
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Abstract:
We first list and state some basic definitions and theorems of the Galois theory of finite extensions, as well as state and prove the Kummer theory and the Artin-Schreier extensions as prerequisites. The main part of this thesis is the proof of the Artin-Schreier Theorem, which states that an algebraic closed field having finite extension with its subfield F has degree at most two and F must have characteristic 0. After the proof, we will discuss the applications for the Artin-Schreier Theorem.
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: Rank-Favorable Bounds for Rational Points on Superelliptic Curves
Defense: Master's
Speaker: Noam Kantor of Emory University
Contact: Noam Kantor, noam.kantor@emory.edu
Date: 2017-04-03 at 3:00PM
Venue: MSC: N304
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Abstract:
Let $C$ be a curve of genus at least two, and let $r$ be the rank of the rational points on its Jacobian. Under mild hypotheses on $r$, recent results by Katz, Rabinoff, Zureick-Brown, and Stoll bound the number of rational points on $C$ by a constant that depends only on its genus. Yet one expects an even stronger bound that depends favorably on $r$: when $r$ is small, there should be fewer points on $C$. In a 2013 paper, Stoll established such a ``rank-favorable" bound for hyperelliptic curves using Chabauty's method. In the present work we extend Stoll's results to superelliptic curves. We also discuss a possible strategy for proving a rank-favorable bound for arbitrary curves based on the metrized complexes of Amini and Baker. Our results have stark implications for bounding the number of rational points on a curve, since $r$ is expected to be small for ``most" curves.
Title: Rank of matrices with few distinct entries
Seminar: Combinatorics
Speaker: Boris Bukh of Carnegie Mellon University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2017-04-03 at 4:00PM
Venue: W303
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Abstract:
Many applications of the linear algebra method to combinatorics rely on bounds on ranks of matrices with few distinct entries and constant diagonal. In this talk, I will explain some of these applications. I will also present a classification of sets \textit{L} for which no low-rank matrix with entries in \textit{L} exists.
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: An Algorithm for Numerically Computing Preimages of the $j$-invariant
Defense: Masters
Speaker: Ethan Alwaise of Emory University
Contact: Ethan Alwaise, ethan.alwaise@emory.edu
Date: 2017-04-05 at 5:30PM
Venue: E408
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Abstract:
Here we explore the problem of numerically computing preimages of the $j$-invariant. We present an algorithm based on studying the asymptotics of the Fourier coefficients of the logarithmic derivative of $j(\tau)$. We use recent work of Bringmann et al., which gives asymptotics for the Fourier coefficients of divisor modular forms, to identify the real and imaginary parts of the preimage.
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