# Seminars archive

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 Upcoming Seminars Tue09/25/20184:00pm Seminar: AlgebraTitle to be announcedRenee Bell, University of PennsylvaniaContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W301Download printable flyer (PDF, 19.8 kB) Mon10/01/20184:00pm Seminar: CombinatoricsOn the Erdos-Gyarfas distinct distances problem with local constraintsCosmin Pohoata, The California Institute of TechnologyContact: Dwight Duffus, dwightduffus@emory.eduVenue: Mathematics and Science Center, Room E408Download printable flyer (PDF, 115 kB)Show abstractIn 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. Tue10/16/20184:00pm Seminar: AlgebraTitle to be announcedEva Bayer Fluckinger, EPFLContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W301Download printable flyer (PDF, 20.3 kB) Tue10/23/20184:00pm Seminar: AlgebraJoint Athens-Atlanta Number Theory SeminarLarry Rolen and Bianca Viray, Vanderbilt and University of WashingtonContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W301Download printable flyer (PDF, 23.7 kB) Tue10/30/20184:00pm Seminar: AlgebraTitle to be announcedAnne Qu\'eguiner-Mathieu, ParisContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W301Download printable flyer (PDF, 19.6 kB) Tue11/27/20184:00pm Seminar: AlgebraTitle to be announcedNatalie Paquette, CaltechContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W301Download printable flyer (PDF, 19.3 kB) Past Seminars 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. Thu02/20/201412:00pm Colloquium: Computer ScienceHarnessing the Power of Crowd for On-Demand Geographical Data CollectionCyrus Shahabi, University of Southern CaliforniaContact: Li Xiong, lxiong@emory.eduVenue: Mathematics and Science Center, Room W303Download attached abstract (PDF, 105 kB)Download printable flyer (PDF, 105 kB)Show abstractGeoCrowd is an online spatial crowdsourcing market (similar to Amazon’s Mechanical Turk) that matches geo tasks (i.e., tasks associated with a specific location and time such as “Take pictures of Tommy Trojan during 2012 USC-UCLA game”) to human workers. Every person with mobile devices can now act as a multi-modal sensor collecting various types of data instantaneously (e.g., picture, video). With GeoCrowd, subscribers can publish tasks with specific space and time attributes. Subsequently, the workers (with GeoCrowd mobile app) can perform the tasks if they are at the right time and at the right place and upload the results to the GeoCrowd server(s). In this talk, I first introduce our generic framework for GeoCrowd and discuss various techniques for optimal assignment of spatiotemporal tasks to human workers. Next, I show how we can extend this framework to incorporate trust in GeoCrowd in order to ensure workers satisfy a confidence value given by the task requester. Finally, I will show an application of the GeoCrowd framework in a commercial domain. Wed02/19/20144:00pm ColloquiumApplications of Flag Algebras in Hypercubes and PermutationsBernard Lidicky, The University of Illinois at Urbana-ChampaignContact: Dwight Duffus, dwight@mathcs.emory.eduVenue: Mathematics and Science Center, Room W303Download printable flyer (PDF, 38.7 kB)Show abstractFlag algebras provide a method, recently developed by Razborov, designed for attacking problems in extremal graph theory. There are recent applications of the method also in discrete geometry or permutation patterns. The aim of talk is to give a gentle introduction to the method and show some of its applications to hypercubes and permutations. The talk is based on joint work with J. Balogh, P. Hu, H. Liu, O. Pikhurko, B. Udvari, and J. Volec. Tue02/18/20144:00pm Seminar: AlgebraLifting Tropical Curves and Linear Systems on GraphsEric Katz, University of WaterlooContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W302Download printable flyer (PDF, 38.4 kB)Show abstractTropicalization is a procedure for associating a polyhedral complex to a subvariety of an algebraic torus. We explain the method of tropicalization and study the question of which graphs arise from tropicalizing algebraic curves. By applying Matthew Baker's technique of specialization of linear systems from curves to graphs, we are able to give a necessary condition for a balanced weighted graph to be the tropicalization of a curve. Our condition is phrased in terms of the harmonic theory of graphs, reproduces the known necessary conditions, and also gives new conditions. Moreover, our method gives a combinatorial way of thinking about the deformation theory of algebraic varieties. Mon02/17/20144:00pm ColloquiumRandomized Block Coordinate Gradient Methods for a Class of Structured Nonlinear ProgrammingZhaosong Lu, Simon Fraser UniversityContact: James Nagy, nagy@mathcs.emory.eduVenue: Mathematics and Science Center, Room W303Download printable flyer (PDF, 41.5 kB)Show abstractNowadays a class of huge-scale structured optimization problems arise in some emerging areas such as machine learning. They can be reformulated as minimizing the sum of a smooth and block separable nonsmooth functions. For these problems, it is prohibitive to evaluate the full gradient of the smooth component of the objective function due to huge dimensionality and hence the usual gradient methods cannot be efficiently applied. Nevertheless, its partial gradients can often be computed much more cheaply. In this talk we study a randomized block coordinate gradient (RBCG) method for solving this class of problems. At each iteration this method randomly picks a block, and solves a proximal gradient subproblem over the subspace defined by the block that only uses a partial gradient and usually has a closed-form solution. We present new iteration complexity results for this method when applied to convex problems. We also propose a nonmonotone RBCG method for solving a class of nonconvex problems with the above structure, and establish their global convergence and iteration complexity. In addition, we present new complexity results for the accelerated RBCG method proposed by Nesterov for solving unconstrained convex optimization problems. Finally, we discuss the application of these methods for solving some support vector machine problems and report some computational results. (This is a joint work with Lin Xiao at Microsoft Research Redmond.) Wed02/12/20144:00pm ColloquiumFast algorithms for electronic structure analysisLin Lin, Lawrence Berkeley National LaboratoryContact: James Nagy, nagy@mathcs.emory.eduVenue: Mathematics and Science Center, Room W303Download printable flyer (PDF, 46.9 kB)Show abstractKohn-Sham density functional theory (KSDFT) is the most widely used electronic structure theory for molecules and condensed matter systems. For a system with N electrons, the standard method for solving KSDFT requires solving N eigenvectors for an $O(N) * O(N)$ Kohn-Sham Hamiltonian matrix. The computational cost for such procedure is expensive and scales as $O(N^3)$. We have developed pole expansion plus selected inversion (PEXSI) method, in which KSDFT is solved by evaluating the selected elements of the inverse of a series of sparse symmetric matrices, and the overall algorithm scales at most $O(N^2)$ for all materials including insulators, semiconductors and metals. The PEXSI method can be used with orthogonal or nonorthogonal basis set, and the physical quantities including electron density, energy, atomic force, density of states, and local density of states are calculated accurately without using the eigenvalues and eigenvectors. The recently developed massively parallel PEXSI method has been implemented in SIESTA, one of the most popular electronic structure software packages using atomic orbital basis sets. The resulting method can allow accurate treatment of electronic structure in a unprecedented scale. We demonstrate the application of the method for solving graphene-like structures with more than 30,000 atoms, and the method can be efficiently parallelized 10,000 - 100,000 processors on Department of Energy (DOE) high performance machines.