# Seminars archive

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 Upcoming Seminars Tue02/27/20184:00pm Colloquium: AlgebraCounting points, counting fields, and heights on stacksJordan Ellenberg, University of Wisconsin-MadisonContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W303Download printable flyer (PDF, 59.6 kB)Show abstractThe basic objects of algebraic number theory are number fields, and the basic invariant of a number field is its discriminant, which in some sense measures its arithmetic complexity. A basic finiteness result is that there are only finitely many degree-$d$ number fields of discriminant at most $X$; more generally, for any fixed global field $K$, there are only finitely many degree-$d$ extensions $L/K$ whose discriminant has norm at most $X$. (The classical case is where $K = \mathbb{Q}$.) \\ When a set is finite, we greedily ask if we can compute its cardinality. Write $N_d(K,X)$ for the number of degree-$d$ extensions of $K$ with discriminant at most $d$. A folklore conjecture holds that $N_d(K,X)$ is on order $c_d X$. In the case $K = \mathbb{Q}$, this is easy for $d=2$, a theorem of Davenport and Heilbronn for $d=3$, a much harder theorem of Bhargava for $d=4$ and 5, and completely out of reach for $d > 5$. More generally, one can ask about extensions with a specified Galois group $G$; in this case, a conjecture of Malle holds that the asymptotic growth is on order $X^a (\log X)^b$ for specified constants $a,b$. \\ I'll talk about two recent results on this old problem: \\ 1) (joint with TriThang Tran and Craig Westerland) We prove that $N_d(\mathbb{F}_q(t),X)) < c_{\epsilon} X^{1+\epsilon}$ for all $d$, and similarly prove Malle’s conjecture up to epsilon" — this is much more than is known in the number field case, and relies on a new upper bound for the cohomology of Hurwitz spaces coming from quantum shuffle algebras: https://arxiv.org/abs/1701.04541 \\ 2) (joint with Matt Satriano and David Zureick-Brown) The form of Malle's conjecture is very reminiscent of the Batyrev-Manin conjecture, which says that the number of rational points of height at most $X$ on a Batyrev-Manin variety also grows like $X^a (\log X)^b$ for specified constants $a,b$. What’s more, an extension of $\mathbb{Q}$ with Galois group $G$ is a rational point on a Deligne--Mumford stack called $BG$, the classifying stack of $G$. A natural reaction is to say “the two conjectures is the same; to count number fields is just to count points on the stack BG with bounded height?” The problem: there is no definition of the height of a rational point on a stack. I'll explain what we think the right definition is, and explain how it suggests a heuristic which has both the Malle conjecture and the Batyrev--Manin conjecture as special cases. Thu03/01/20183:00pm Defense: DissertationOn Cycles, Chorded Cycles, and Degree ConditionsAriel Keller, Emory UniversityContact: Ariel Keller, ariel.keller@emory.eduVenue: MSC N301Download printable flyer (PDF, 50.4 kB)Show abstractSufficient conditions to imply the existence of certain substructures in a graph are of considerable interest in extremal graph theory, and conditions that guarantee a large set of cycles or chorded cycles are a recurring theme. This dissertation explores different degree sum conditions that are sufficient for finding a large set of vertex-disjoint cycles or a large set of vertex-disjoint chorded cycles in a graph. \vskip.1in For an integer $t\ge 1$, let $\sigma_t (G)$ be the smallest sum of degrees of $t$ independent vertices of $G$. We first prove that if a graph $G$ has order at least $7k+1$ and degree sum condition $\sigma_4(G)\ge 8k-3$, with $k\ge 2$, then $G$ contains $k$ vertex-disjoint cycles. Then, we consider an equivalent condition for chorded cycles, proving that if $G$ has order at least $11k+7$ and $\sigma_4(G)\ge 12k-3$, with $k\ge 2$, then $G$ contains $k$ vertex-disjoint chorded cycles. We prove that the degree sum condition in each result is sharp. Finally, we conjecture generalized degree sum conditions on $\sigma_t(G)$ for $t\ge 2$ sufficient to imply that $G$ contains $k$ vertex-disjoint cycles for $k \ge 2$ and $k$ vertex-disjoint chorded cycles for $k \ge 2$. This is joint work with Ronald J. Gould and Kazuhide Hirohata. Tue03/27/20184:00pm Seminar: AlgebraTitle to be announcedNathan Kaplan, UC IrvineContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W304Download printable flyer (PDF, 19.2 kB) Mon04/02/20184:00pm Defense: DissertationPatching and local-global principles for gerbes with an application to homogeneous spacesBastian Haase, Emory UniversityContact: Bastian Haase, bastian.haase@emory.eduVenue: Mathematics and Science Center, Room W302Download printable flyer (PDF, 44.9 kB)Show abstractStarting in 2009, Harbater and Hartmann introduced a new patching setup for semi-global fields, establishing a patching framework for vector spaces, central simple algebras, quadratic forms and other algebraic structures. In subsequent work with Krashen, the patching framework was refined and extended to torsors and certain Galois cohomology groups. After describing this framework, we will discuss an extension of the patching equivalence to bitorsors and gerbes. Building up on these results, we then proceed to derive a characterisation of a local- global principle for gerbes and bitorsors in terms of factorization. These results can be expressed in the form of a Mayer-Vietoris sequence in non-abelian hypercohomology with values in the crossed-module $G->Aut(G)$. After proving the local-global principle for certain bitorsors and gerbes using the characterization mentioned above, we conclude with an application on rational points for homogeneous spaces. Tue04/03/20184:00pm Seminar: AlgebraTitle to be announcedJennifer Berg, RiceContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W304Download printable flyer (PDF, 19.4 kB) Thu04/05/20184:00pm ColloquiumTitle to be announcedSherry Li, Lawrence Berkeley National LabContact: Lar Ruthotto, lruthotto@emory.eduVenue: Mathematics and Science Center, Room W201Download printable flyer (PDF, 19.3 kB) Thu04/12/20184:00pm Colloquium: AlgebraTitle to be announcedK. Soundararajan, Stanford UniversityContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W304Download printable flyer (PDF, 19.7 kB) Tue04/17/20184:00pm Seminar: AlgebraTitle to be announcedBrandon William, UC BerkeleyContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W304Download printable flyer (PDF, 19.1 kB) Tue04/24/20184:00pm Seminar: AlgebraTitle to be announcedFrank Thorne, University of South CarolinaContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W304Download printable flyer (PDF, 19.3 kB) Past Seminars Tue03/04/20144:00pm Seminar: Analysis and Differential GeometryTwo-Hilbert spaces Mourre theory for the Laplace-Beltrami operator on manifolds with asymptotically cylindrical endsRafael Tiedra de Aldecoa, Catholic University of ChileContact: David Borthwick, davidb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W301Download printable flyer (PDF, 38.8 kB)Show abstractWe review some aspects of Mourre theory in a two-Hilbert spaces setting. Then we apply this theory to the spectral analysis for the Laplace-Beltrami operator on manifolds with asymptotically cylindrical ends. This is a joint work with Serge Richard (University of Nagoya). Mon03/03/20144:00pm ColloquiumWhen Big Data Meets BRAIN Initiative: Large-Scale Structured Sparse Learning with Applications in Imaging GenomicsHeng Huang, University of Texas at ArlingtonContact: Vaidy Sunderam, vss@emory.eduVenue: Mathematics and Science Center, Room W303Download printable flyer (PDF, 43.1 kB)Show abstractSparsity is one of the intrinsic properties of real-world data, thus sparse machine learning has recently emerged as powerful tool to obtain models of high-dimensional data with high degree of interpretability at low computational cost, and provide great opportunities to analyze the big, complex, and diverse datasets. By enforcing properly designed structured sparsity, we can integrate the specific data structures and domain knowledge into the machine learning models to simplify data models and discover predictive patterns in big data analytics. Big Data research is accelerating the translation of biological and biomedical data to advance the detection, diagnosis, treatment and prevention of diseases, including the recently announced BRAIN (Brain Research through Advancing Innovative Neurotechnologies) Initiative. To address the challenging problems in current big data mining, we proposed several novel large-scale structured sparse learning models for multi-dimensional data integration, heterogeneous multi-task learning, group/graph structured data analysis, and longitudinal feature learning. We applied our new structured sparse learning models to analyze the multi-modal neuroimaging and genome-wide array data in Imaging Genomics and discover the phenotypic and genotypic biomarkers to characterize the neurodegenerative process in the progression of Alzheimer’s disease and other complex brain disorders. We also utilized our new machine learning models to analyze the Electronic Medical Records for predicting the heart failure patients’ readmission and drug side effects, detect the multi-dimensional biomarkers in The Cancer Genome Atlas (TCGA) research, and identify the brain circuitry patterns in Human Connectome. Fri02/28/201411:00am Seminar: Computer ScienceAn Integrated Human Decision Making Model under Extended Belief-Desire-Intention Framework: Emergency Evacuation ApplicationsYoung-Jun Son, The University of ArizonaVenue: Mathematics and Science Center, Room W303Download printable flyer (PDF, 42.3 kB)Show abstractIn this talk, we discuss an integrated Belief-Desire-Intention (BDI) modeling framework for human decision making, whose sub-modules are based on Bayesian belief network, Decision-Field-Theory, and probabilistic depth first search technique. A key novelty of the proposed model is its ability to represent both the human decision-making and decision-planning functions in a unified framework. In this talk, the proposed modeling framework is demonstrated for human’s evacuation behaviors under a terrorist bomb attack situation. To mimic realistic human behaviors, attributes of the BDI framework are reverse-engineered from the human-in-the-loop experiments conducted in the Cave Automatic Virtual Environment (CAVE) available at The University of Arizona. A crowd simulation is then constructed, where individual human behaviors are based on what was learned from the CAVE experiments. In this work, the simulated environment and humans conforming to the proposed BDI framework are implemented in AnyLogic® agent-based simulation software, where each human entity calls external Netica BBN software to perform its perceptual processing function and Soar software to perform its real-time planning and decision-execution functions. The constructed crowd simulation is then used to test impact of several factors (e.g. demographics of people, number of policemen, information sharing via speakers) on evacuation performance (e.g. average evacuation time, percentage of casualties). Finally, we discuss other emergency evacuation applications (e.g. evacuation behaviors under fire in a factory) and research extensions for the proposed BDI framework. Thu02/27/20144:00pm ColloquiumAssured Information Distillation in Social SensingDong Wang, University of Illinois at Urbana-ChampaignContact: Vaidy Sunderam, vss@emory.eduVenue: Mathematics and Science Center, Room W306Download printable flyer (PDF, 38.8 kB)Show abstractThe advent of sensors and online social broadcast media (e.g., Twitter and Flickr) create a deluge of unfiltered, unstructured, and unvetted data about the physical environment. This opens up unprecedented challenges and opportunities in social sensing, where the goal is to distill assured information from social sources and devices in their possession. This talk will present a new analytical framework and theories to obtain reliable information with quality guarantees from large amounts of unreliable social sensing data. Noticeably, our analytical framework is the first to jointly model the complex interactions among three deeply coupled networks underlying the data; namely, the information, social and physical networks. The talk will also introduce a new information distillation system we built, called Apollo, which has been applied in a wide range of social sensing scenarios such as real event/disaster tracking, geo-tagging, smart road applications, and language/dialect classification. Apollo is now used by different branches at Army Research Lab (ARL). Tue02/25/20145:15pm Seminar: Joint Athens-Atlanta Number Theory SeminarBounded gaps between primesJames Maynard, Universite de MontrealContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W302Download printable flyer (PDF, 48.4 kB)Show abstractIt is believed that there should be infinitely many pairs of primes which differ by 2; this is the famous twin prime conjecture. More generally, it is believed that for every positive integer $m$ there should be infinitely many sets of $m$ primes, with each set contained in an interval of size roughly $m\log{m}$. We will introduce a refinement of the `GPY sieve method' for studying these problems. This refinement will allow us to show (amongst other things) that $\liminf_n(p_{n+m}-p_n)<\infty$ for any integer $m$, and so there are infinitely many bounded length intervals containing $m$ primes. Tue02/25/20144:00pm Seminar: Joint Athens-Atlanta Number Theory SeminarSolved and unsolved problems in elementary number theoryPaul Pollack, UGAContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W302Download printable flyer (PDF, 37.6 kB)Show abstractThis will be a survey of certain easy-to-understand problems in elementary number theory about which "not enough" is known. We will start with a discussion of the infinitude of primes, then discuss the ancient concept of perfect numbers (and related notions), and then branch off into other realms as the spirit of Paul Erd\H{o}s leads us. Tue02/25/20144:00pm ColloquiumDiscourse-Guided and Multi-faceted Event Recognition from TextRuihong Huang, University of UtahContact: Vaidy Sunderam, vss@emory.eduVenue: Mathematics and Science Center, Room W303Download printable flyer (PDF, 40.7 kB)Show abstractEvents are one important type of information throughout the text. Accurately extracting significant events from large volumes of text informs the government, companies and the public regarding possible changing circumstances caused or implied by events. \\ \\ Extracting event information completely and accurately is challenging mainly due to the high complexity of discourse phenomena. In this talk, I will present two discourse-guided event extraction architectures that explore evidence and clues from wider discourse to seek out or validate pieces of event descriptions. TIER is a multilayered event extraction architecture that performs text analysis at multiple granularities to progressively "zoom in" on relevant event information. LINKER is a more principled discourse-guided approach that models textual cohesion properties in a single structured sentence classifier.\\ \\ Finding documents that describe a specific type of event is also challenging because of the wide variety and ambiguity of event expressions. I will focus on the recent multi-faceted event recognition approach that uses event defining characteristics (facets), in addition to event expressions, to effectively resolve the complexity of event descriptions. I will present a novel bootstrapping algorithm that can automatically learn both event expressions and facets from unannotated texts, which will enable fast configurations of domain-specific event detection systems. Mon02/24/20144:00pm ColloquiumDynamic Performance Profiling of Data CachesYmir Vigfusson, Reykjavik UniversityContact: Vaidy Sunderam, vss@emory.eduVenue: Mathematics and Science Center, Room W303Download printable flyer (PDF, 41.2 kB)Show abstractScalable data replication protocols and layers, such as streaming, multicast and caching, enable large data-driven distributed systems to be practical. As a concrete example, large-scale in-memory object caches like memcached are now widely used to accelerate popular web sites and to reduce burden on backend databases. Yet operators still have limited visibility into how these caches should be set up to optimally accommodate the workloads they see. How much would the cache performance improve from additional cache space, or by adding more cache servers to the pool? Since resources come at a cost, to what extent would request latencies deteriorate if cache memory were repurposed for a different service?\\ \\ In this talk, I'll focus on some of the latest research questions pertaining to scalable data replication and large-scale distributed caches. In particular, I'll home in on the challenge of providing online monitoring of the cost and benefits of memory space in a large-scale cache, enabling cache operators to answer the questions above without requiring extraneous trace collection and manual offline tuning. I will introduce general and efficient algorithms for dynamically estimating hit rate curves -- histograms of cache hit rate as a function of memory size -- which can be plugged into cache replacement policies such as LRU.\\ \\ Extensive simulations on cache benchmarks indicate that these methods provide accurate estimates of hit rate at different cache sizes. Experiments on an implementation of these methods in memcached showed that hit rate curves were dynamically estimated at over 98% accuracy with only a small drop in throughput. The results are encouraging and suggest that exposing hit rate curves can be a practical method for improving provisioning and metering of large-scale data caches. Fri02/21/20143:00pm ColloquiumDecision Making and Inference under Limited Information and Large DimensionalityStefano Ermon, Cornell UniversityContact: Vaidy Sunderam, vss@emory.eduVenue: Mathematics and Science Center, Room W201Download printable flyer (PDF, 38.4 kB)Show abstractStatistical inference in high-dimensional probabilistic models (i.e., with many variables) is one of the central problems of statistical machine learning and stochastic decision making. To date, only a handful of distinct methods have been developed, most notably (MCMC) sampling, decomposition, and variational methods. In this talk, I will introduce a fundamentally new approach based on random projections and combinatorial optimization. Our approach provides provable guarantees on accuracy, and outperforms traditional methods in a range of domains, in particular those involving combinations of probabilistic and causal dependencies (such as those coming from physical laws) among the variables. This allows for a tighter integration between inductive and deductive reasoning, and offers a range of new modeling opportunities. As an example, I will discuss an application in the emerging field of Computational Sustainability aimed at discovering new fuel-cell materials where we greatly improved the quality of the results by incorporating prior background knowledge of the physics of the system into the model. Thu02/20/20144:00pm ColloquiumExtremal problems on optimizing the number of nonnegative subsetsHao Huang, The Institute for Advanced Study and DIMACSContact: Dwight Duffus, dwight@mathcs.emory.eduVenue: Mathematics and Science Center, Room W301Download printable flyer (PDF, 37.7 kB)Show abstractExtremal combinatorics studies the maximum or minimum possible size of a combinatorial structure satisfying certain properties. It is one of the central themes of modern discrete mathematics, and has numerous natural connections to other areas including probability, number theory and theoretical computer science. As an example, in this talk I will discuss some recent progress on a fifty-year-old conjecture of Erdos on hypergraph matching, and describe its relation with several other extremal problems on optimizing the number of nonnegative. Our work settles conjectures of Manickam, Miklos and Singhi, and of Tsukerman.