All Seminars

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Title: TBA
Colloquium: N/A
Speaker: Sherry Li of Lawrence Berkeley National Lab
Contact: Lar Ruthotto, lruthotto@emory.edu
Date: 2018-04-05 at 4:00PM
Venue: W201
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Abstract:
TBA
Title: Patching for proper schemes
Seminar: Algebra
Speaker: Bastian Haase of Emory University
Contact: John Duncan, john.duncan@emory.edu
Date: 2017-12-05 at 4:00PM
Venue: W306
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Abstract:
We discuss an extension of field patching to proper schemes. Then, we will introduce Tannaka duality for stacks as first developed by Lurie and then refined by Hall and Rydh. Their work allows us to patch morphisms from proper schemes to nice stacks, in particular certain moduli stacks. As an application of this result, we prove that patching holds for relative torsors which allows us to give a characterization for local-global principles for torsors over proper schemes. This is joint work with Daniel Krashen and Max Lieblich.
Title: The complexity of perfect matchings and packings in dense hypergraphs
Seminar: Combinatorics
Speaker: Jie Han of University of Sao Paulo
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2017-12-04 at 4:00PM
Venue: W302
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Abstract:
Given two $k$-graphs $H$ and $F$, a perfect $F$-packing in $H$ is a collection of vertex-disjoint copies of $F$ in $H$ which together cover all the vertices in $H$. In the case when $F$ is a single edge, a perfect $F$-packing is simply a perfect matching. For a given fixed $F$, it is generally the case that the decision problem whether an $n$-vertex $k$-graph $H$ contains a perfect $F$-packing is NP-complete.\\ \\In this talk we describe a general tool which can be used to determine classes of (hyper)graphs for which the corresponding decision problem for perfect $F$-packings is polynomial time solvable. We then give applications of this tool. For example, we give a minimum $l$-degree condition for which it is polynomial time solvable to determine whether a $k$-graph satisfying this condition has a perfect matching (partially resolving a conjecture of Keevash, Knox and Mycroft). We also answer a question of Yuster concerning perfect $F$-packings in graphs.
Title: Recommender System and Information Fusion in Spatial Crowdsourcing
Defense: Dissertation
Speaker: Daniel Garcia Ulloa of Emory University
Contact: TBA
Date: 2017-12-01 at 11:00AM
Venue: W301
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Abstract:
Spatial Crowdsourcing (SC) refers to a series of data collection mechanisms where a set of users with a sensing or computing device are asked to perform a set of tasks at different locations and times.\\ \\In this work, we explore some of the challenges that arise with SC and propose some solutions. These challenges concern a proper recommendation of tasks to users in such a away that they maximize their expected utility while at the same time maximizing the probability that all the tasks are performed. The utility for the users can be based on the tasks the expected reward they are planning to obtain, and the distance to the assignments. These aspects can be predicted through tensorfactorization techniques. To set an example, a high-paying assignment might be far from a user, while a low paying assignment is nearby. Depending on the users’ preference, we seek to recommend a set of tasks that maximize the user’s utility. On the other hand, we also want to maximize the sum of probabilities that the tasks are performed, considering the interdependencies between users. We define the system utility as a convex linear combination of the user and the task utility and suggest approximation methods to recommend the tasks that yield the highest system utility.\\ \\We also deal with the problem of truth inference, which focuses on integrating the responses from a mobile crowdsouring scenario and determining the true value. Many times, the answers from a mobile crowdsourcing scenario are noisy, contradicting or have missing values. We developed a recursive Bayesian system that updates the reputation model of the users, the probability that the users where in the correct time and location, and the probability that the reports are true or false. We further enhanced this algorithm using a Kalman filter that predicts the true state of the event at each time-stamp using a hidden event model and which is updated with the reports from the users. Our method was compared against the naive majority voting method as well as other state-of-the-art truth inference algorithms and our method shows a considerable improvement.
Title: Bridging the Gap: Math across Emory
Seminar: Numerical Analysis and Scientific Computing
Speaker: Samuel Sober, Roberto Franzosi, Gordon Berman of Emory University
Contact: Sofia Guzzetti, sofia.guzzetti@emory.edu
Date: 2017-11-17 at 2:00PM
Venue: W301
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Abstract:
Mathematics is a powerful tool that addresses real-life applications arising from various disciplines. In this event, organized by the Emory SIAM Student Chapter, you will be able to taste the versatility of Math. Professors conducting cutting-edge research in Biology, Sociology, and Physics will share how Mathematics contributes to their work. The talks will be followed by an open discussion and refreshments.
Title: Application of Global Optimization to Image Registration
Defense: Honors Thesis
Speaker: Huiying Zhu of Emory University
Contact: TBA
Date: 2017-11-16 at 2:30PM
Venue: E408
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Abstract:
Given two images, image registration aims to transform an image into a given reference image so that the two images look alike. This technique is vital in many applications, such as medical imaging and astronomy. Finding the best transform can be phrased as solving a mathematical optimization problem. Due to the non-convexity of the objective function, commonly employed optimization techniques often generate local minimizers, limiting the accuracy of the registration. This thesis evaluates the applicability of a global optimization method, called as DDNCID, for image registration. Direct application of DDNCID in image registration could cause minimizers to be infeasible. Thus, a focus of this thesis is to add a bound constraint by imposing a barrier function into the objective function to extend DDNCID.
Title: An arithmetic count of the lines on a cubic surface.
Seminar: Algebra
Speaker: Kirsten Wickelgren of Georgia Institute of Technology
Contact: John Duncan, john.duncan@emory.edu
Date: 2017-11-14 at 4:00PM
Venue: W306
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Abstract:
A celebrated 19th century result of Cayley and Salmon is that a smooth cubic surface over the complex numbers contains exactly 27 lines. Over the real numbers, it is a lovely observation of Finashin–Kharlamov and Okonek–Teleman that while the number of real lines depends on the surface, a certain signed count of lines is always 3. We extend this count to an arbitrary field k using an Euler number in A1-homotopy theory. The resulting count is valued in the Grothendieck-Witt group of non-degenerate symmetric bilinear forms. This is joint work with Jesse Kass.
Title: On semi-simplicity of tensor products in positive characteristics
Seminar: Algebra
Speaker: Vikraman Balaji of Chennai Mathematical Institute
Contact: John Duncan, john.duncan@emory.edu
Date: 2017-11-14 at 5:00PM
Venue: W306
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Abstract:
We work over an algebraically closed field k of characteristic p greater than 0. In 1994, Serre showed that if semi-simple representations V_i of a group \Gamma are such that \sum ( dim(V_i) - 1 ) less than p, then their tensor product is semi-simple. In the late nineties, Serre generalized this theorem comprehensively to the case where \Gamma is a subgroup of G(k), for G a reductive group, and answered the question of “complete reducibility” of \Gamma in G (Seminaire Bourbaki, 2003). In 2014, Deligne generalized the results of Serre (of 1994) to the case when the V_i are semi-simple representations of a group scheme \mathfrak{G}. In my talk I will present the recent work of mine with Deligne and Parameswaran where we consider the case when \mathfrak{G} is a subgroup scheme of a reductive group G and generalize the results of Serre and Deligne. A key result is a structure theorem on “doubly saturated” subgroup schemes \mathfrak{G} of reductive groups G. As an application, we obtain an analogue of classical Luna's etale slice theorem in positive characteristics.
Title: Ramsey Properties of Random Graphs and Hypergraphs
Seminar: Combinatorics
Speaker: Andrzej Dudek of Western Michigan University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2017-11-13 at 4:00PM
Venue: W302
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Abstract:
TBA
Title: Accelerated Diffeomorphisms for Motion Estimation and Segmentation from Video
Seminar: Numerical Analysis and Scientific Computing
Speaker: Ganesh Sundaramoorthi of KAUST
Contact: James Nagy, nagy@mathcs.emory.edu
Date: 2017-11-10 at 2:00PM
Venue: W301
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Abstract:
Accelerated optimization methods have gained wide applicability within the machine learning and optimization communities. They are known for leading to optimal convergence rates among schemes that use only use gradient (first order) information in the convex case. In the non-convex case, they appear to provide robustness to shallow local minima. The intuitive idea is that by considering a particle with mass that moves in an energy landscape, the particle will gain momentum and surpass shallow local minimum and settle in in more wider, deeper local extrema in the energy landscape. Although these techniques have been widely used, it was only within the last few years that theoretical attempts have been made to understand them and put them in a mathematical framework. Recent work has shown that accelerated methods may be formulated with variational principles, although in finite dimensions. Motivated by the success of accelerated methods in finite dimensional problems, we formulate optimization problems on infinite dimensional manifolds of diffeomorphisms using a generalization of this approach. The talk will mainly be about the mathematical formulation and some simple examples to illustrate the advantages of this approach. We note very large speed-ups in optical flow computation compared with standard approaches, and robustness to local minimum. Finally, we outline considerations for generalizing this approach to video data and applications in motion-based object segmentation, which require one to optimize diffeomorphisms not just defined on the image domain, but evolving regions of interest that encompass the domain of each of the objects in the scene.\\ \\Bio: Ganesh Sundaramoorthi received the PhD in Electrical and Computer Engineering from Georgia Institute of Technology, Atlanta, USA, and BS in Computer Engineering and BS Mathematics from the same institution in 2003. He was then a postdoctoral researcher in the Computer Science Department at the University of California, Los Angeles between 2008 and 2010. In 2011, he was appointed Assistant Professor of Electrical Engineering and Assistant Professor of Applied Mathematics and Computational Science at King Abdullah University of Science and Technology (KAUST). His research interests include computer vision and its mathematical foundations with recent interest in shape and motion analysis, video analysis, invariant representations for visual tasks, and applications. He was an area chair for IEEE ICCV 2017 and IEEE CVPR 2018.