Skip to main content Skip to footer site map
Mathematics Department

Colloquium Series

Fall 2015

All talks are from 3:45-4:45 p.m. in the Colloquium Room, unless otherwise specified.

  • Dec
    10
  • A New Approach to Visualizing and Clustering Mixed Categorical and Numeric Data
    Prof. Sam Buttrey
    Naval Postgraduate School
    Time: 03:45 PM

    View Abstract

    The job of measuring distances or dissimilarities between observations is critical in tasks like clustering, collaborative filtering, and pattern recognition. An inter-observation dissimilarity should account for categorical variables, scale numeric ones, protect against distortion from outliers, remove noisy or redundant variables, and handle missing values gracefully. We propose such a dissimilarity based on a set of classification and regression trees (which we review briefly). Our dissimilarity performs better than competitors in the face of noise and outliers, and can be scaled to large data. Some visualizations are presented.
  • Dec
    09
  • Determining a Discrete Set of Site-Constrained Privacy Options for Users in Social Networks through Stackelberg Games
    Prof. Sarah Rajtmajer
    Penn State University
    Time: 03:45 PM

    View Abstract

    The privacy policies of an online social network play an important role in determining user involvement and satisfaction, and in turn site profit and success. In this talk, we present a game theoretic framework to model the relationship between the set of privacy options offered by a social network site and the sharing decisions of its users within these constraints. We model the site and the users in this scenario as the leader and followers, respectively, in a Stackelberg game. We formally establish the conditions under which this game reaches a Nash equilibrium in pure strategies and provide an approximation algorithm for the site to determine a discrete set of privacy options to maximize payoff. We validate hypotheses in our model on data collected from a mock-social network of users' privacy preferences both within and outside the context of peer influence, and demonstrate that the qualitative assumptions of our model are well-founded.
  • Dec
    02
  • Linear Programming Games with Risk-Averse Players
    Time: 03:45 PM

    View Abstract

    Joint work with Alejandro Toriello (Georgia Tech) In many situations, a group of individuals may benefit from cooperating and participating in a joint enterprise, even if they do not share a common objective. In order for such a partnership to be successful, the participants must agree on how to share the costs they incur together. Cooperative game theory provides a mathematical framework for determining "fair" ways of sharing these costs of cooperation. In this work, we introduce and study dynamic linear programming games, a class of cooperative games in which the costs of cooperation are uncertain and evolve over time. These games generalize the well-studied linear programming game, and as a result, model a variety of cost sharing settings. We model players' attitudes towards risk using dynamic risk measures formed from conditional risk mappings. We give structural and algorithmic results for the strong sequential core, the set of allocations that distribute costs as they are incurred and are stable against coalitional defections at any point in time.
  • Nov
    13
  • Prediction and quantification of rare events in nonlinear water waves
    Time: 12:00 PM

    View Abstract

    The scope of this work is the development, application, and demonstration of probabilistic methods for the prediction and quantification of extreme events occurring in complex nonlinear systems involving water waves. Although rare these transitions can occur frequently enough so that they can be considered of critical importance. We are interested to address two specific issues related to rare events: i) short term prediction given measurements of specific quantities about the current system state (Rare Event Prediction Problem); and ii) quantification of the probability of occurrence of a rare event for a given energetic regime of the system (Rare Event Quantification Problem). We first analytically quantify the role of spatial energy localization on the development of nonlinear instabilities and the subsequent formation of rare events in water waves. We then prove that these localized instabilities are triggered through the dispersive ‘heat bath’ of random waves that propagate in the nonlinear wave field. The interaction of uncertainty induced through the dispersive wave mixing and nonlinear wave-wave instability defines a critical length-scale for the formation of rare events. To tackle the first problem we rely on this property and show that by merely tracking the energy of the wave field over this critical length-scale allows for the robust, inexpensive prediction of the location of intense waves with a prediction window of 25 wave periods. For the second problem, we also utilize the nonlinear stability analysis to decompose the state space into regions where rare events is unlikely to occur and regions that lead with high probability to the occurrence of a rare event. The two regions are treated differently and the information of the two regimes is merged through a total probability argument, allowing for the efficient quantification of rare events.
  • Nov
    04
  • Bad Company: Reconciling Negative Peer Effects in College Achievement
    Prof. Mike Insler
    USNA (Economics)
    Time: 03:45 PM

    View Abstract

    Existing peer effects studies produce contradictory findings, including positive, negative, large, and small effects, despite similar contexts. We reconcile these results using U.S. Naval Academy data covering a 22-year history of the random assignment of students to peer groups. Coupled with students' limited discretion over freshman-year courses, our setting affords an opportunity to better understand peer effects in different social networks. We find negative effects at the broader “company” level---students' social and residential group---and positive effects at the narrower course-company level. We suggest that peer spillovers change direction because of differences in the underlying mechanism of peer influence.
  • Oct
    21
  • Galois representations
    Prof. David Savitt
    Johns Hopkins University
    Time: 03:45 PM

    View Abstract

    The absolute Galois group of the field of rational numbers is a fundamental object of study in number theory. I will begin by giving a tour of the representation theory of this group, with an emphasis on representations in characteristic p. In the second part of the talk I will describe my recent work with Gee, Liu, and others on generalizations of the weight part of Serre's conjecture on two-dimensional mod p Galois representations.
  • Oct
    14
  • Post-Quantum Cryptography
    Prof. Timothy Hodges
    University of Cincinnati
    Time: 03:45 PM

    View Abstract

    A review of the general situation and some discussion about the mathematical problems that arise.
  • Oct
    07
  • Trade, Technology, and the Great Divergence
    Prof. Ahmed Rahman
    USNA (Economics)
    Time: 03:45 PM

    View Abstract

    This paper develops a model that captures the key features of the Industrial Revolution and the Great Divergence between the industrializing "North" and the lagging "South." In particular, a convincing story is needed for why North-South divergence occurred so dramatically during the late 19th Century, a good hundred years after the beginnings of the Industrial Revolution. To this end we construct a trade/growth model that includes both endogenous biased technologies and intercontinental trade. The Industrial Revolution began as a sequence of unskilled-labor intensive innovations which initially incited fertility increases and limited human capital formation in both the North and the South. The subsequent co-evolution of trade and technological growth however fostered an inevitable divergence in living standards. The model highlights how pronounced divergence ultimately arose from interactions between specialization from trade and technological forces.
  • Sep
    23
  • The Kazhdan-Lusztig polynomial of a matroid
    Time: 03:45 PM

    View Abstract

    We study a few different perspectives (combinatorics, geometry, and algebra) of a new polynomial attached to a matroid. First we define the polynomial combinatorially and compute it for certain examples. Then we will discuss how the polynomial arose out of the study of the intersection cohomology of the reciprocal plane (i.e. the Spectrum of the Orlik-Terao algebra). If time permits we will discuss an algebraic interpretation through a deformed Mobius algebra. This polynomial closely resembles the Kazhdan-Lusztig polynomial attached to a Coxeter group. Though there are significant differences, the similarities are striking.
  • Sep
    16
  • Dynamical behaviors Typically seen: Chaos and Quasiperiodicity
    Prof. James Yorke
    University of Maryland
    Time: 03:45 PM
  • Sep
    09
  • Implementation of Assortative Matching Under Incomplete Information
    Prof. Naomi Utgoff
    USNA (Economics)
    Time: 03:45 PM

    View Abstract

    This paper provides a unifying framework for matching markets with incomplete information, when the positive assortative match is the unique efficient stable match. I construct a second-price-like auction mechanism which implements assortative matching as an ex post Nash equilibrium. It achieves this result using a payment rule that distinguishes between an agent deprived of any match and an agent who merely receives a reduced match surplus. The constructed mechanism recognizes only opportunity costs arising from the former, and not the latter, effect.
go to Top