BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Edgar Costa (MIT) DTSTART:20211203T190000Z DTEND:20211203T200000Z DTSTAMP:20260422T212927Z UID:WMmathcolloq/1 DESCRIPTION:Title: The L-functions and modular forms database\nby Edgar Costa (MIT) as part of William & Mary Mathematics Colloquium\n\n\nAbstract\nThe Langla nds program\, first formulated by Robert Langlands in the 1960s and since much developed and refined\, is a web of widespread conjectures that lie i n deep theories of mathematical symmetry\, it gives schematic direction to navigate between a dizzying array of subfields of mathematics\, including number theory\, representation theory\, algebraic geometry\, and harmonic analysis\nIn this talk\, we will explore some of these objects and connec tions and introduce the L-Functions and modular forms database (LMFDB) at https://www.lmfdb.org/\, as one of it s goals is to provide a compelling visualization for the connections predi cted by the Langlands program.\nFor example\, we will see how the Riemann hypothesis\, Goldbach's conjecture\, and Fermat's last theorem are related .\n LOCATION:https://researchseminars.org/talk/WMmathcolloq/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Herbert Chang (University of Southern California) DTSTART:20220225T190000Z DTEND:20220225T200000Z DTSTAMP:20260422T212927Z UID:WMmathcolloq/2 DESCRIPTION:Title: Fields Medals Are Concentrated in Mathematical ‘Families’\nby Herbert Chang (University of Southern California) as part of William & Ma ry Mathematics Colloquium\n\n\nAbstract\nThe Fields Medal\, often referred as the Nobel Prize of mathematics\, is awarded to no more than four mathe maticians under the age of 40\, every 4 years. In recent years\, its confe rral has come under scrutiny of math historians\, for rewarding the existi ng elite rather than its original goal of elevating under-represented math ematicians. Prior studies of elitism focus on citational practices while c haracterization of the structural forces that prevent access remain unclea r. Here we show the flow of elite mathematicians between countries and lin go-ethnic identity\, using network analysis and natural language processin g on 240\,000 mathematicians and their advisor–advisee relationships. We present quantitative evidence of how the Fields Medal helped integrate Ja pan after WWII\, through analysis of the elite circle formed around Fields Medalists. We show increases in pluralism among major countries\, though Arabic\, African\, and East Asian identities remain under-represented at t he elite level. Our results demonstrate concerted efforts by academic comm ittees\, such as prize giving\, can either reinforce the existing elite or reshape its definition. We anticipate our methodology of academic genealo gical analysis can serve as a useful diagnostic for equity and systemic bi as within academic fields. The presentation will also briefly discuss the similar use of network science and graph theory in profiling misinformatio n during the Covid-19 pandemic.\n LOCATION:https://researchseminars.org/talk/WMmathcolloq/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Dana P. Williams (Dartmouth College) DTSTART:20220304T190000Z DTEND:20220304T200000Z DTSTAMP:20260422T212927Z UID:WMmathcolloq/3 DESCRIPTION:Title: The Equivalence Theorem for groupoid C*-algebras\nby Dana P. Will iams (Dartmouth College) as part of William & Mary Mathematics Colloquium\ n\n\nAbstract\nOne of the original motivations for the study of C*-algebra s came from noncommutative harmonic analysis and the group C*-algebra cons truction. Nowadays the representation theory of C*-algebras is an interes ting subject onto itself. An essential tool is the notion of Morita equiv alence of C*-algebras which is a good deal coarser than isomorphism\, but still implies an equivalence of the representation theory. There are many ways to build C*-algebras mimicing the group C*-algebra construction and a key player is the construction of C*-algebras from groupoids. Some time ago\, Jean Renault observed that a notion of groupoid equivalence implied Morita equivalence of the corresponding C*-algebras which gives a very co ncrete and topological way to establish deep analytic facts. After briefl y outlining the necessary background\, I will give a sketch of this Equiva lence Theorem using a newer proof developed by Aidan Sims and myself.\n LOCATION:https://researchseminars.org/talk/WMmathcolloq/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Mahlet Tadesse (Georgetown University) DTSTART:20220325T180000Z DTEND:20220325T190000Z DTSTAMP:20260422T212927Z UID:WMmathcolloq/4 DESCRIPTION:Title: Uncovering cluster structures and relevant biomarkers in “-omics” data\nby Mahlet Tadesse (Georgetown University) as part of William & Mary Mathematics Colloquium\n\n\nAbstract\nHigh-throughput “-omics” te chnologies (genomics\, epigenomics\, transcriptomics\, proteomics\, metabo lomics\, etc) allow the simultaneous quantification of thousands of biomar kers. These technologies hold great potential for gaining insights into th e complex biological processes underlying specific phenotypes and for iden tifying biomarkers that can be used for improved diagnosis and therapeutic interventions. The challenges of analyzing the generated data have led to the development of various statistical\, computational and bioinformatic tools over the the past couple of decades. In this talk\, I will present s ome of the methods we have proposed for uncovering cluster structures and relevant biomarkers by combining ideas of mixture models and variable sele ction. I will discuss (1) a bi-clustering approach that allows clustering on subsets of variables to refine disease classes and identify discriminat ing biomarkers\, (2) an integrative model to relate data from different -o mic levels using a stochastic partitioning method\, and (3) a mixture of r egression trees approach to uncover homogeneous disease subgroups and thei r associated predictors accounting for non-linear relationships and intera ction effects. I will illustrate the methods on various -omic studies.\n LOCATION:https://researchseminars.org/talk/WMmathcolloq/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Tai Melcher (University of Virginia) DTSTART:20220408T180000Z DTEND:20220408T190000Z DTSTAMP:20260422T212927Z UID:WMmathcolloq/5 DESCRIPTION:Title: Hypoellipticity in infinite dimensions\nby Tai Melcher (Universit y of Virginia) as part of William & Mary Mathematics Colloquium\n\n\nAbstr act\nConsider a flat infinite surface to which one applies a unit of heat at a fixed point and then steps away allowing the heat to propagate. The h eat flows quickly at first and then ever more slowly as it converges every where to zero. Contrast this now with the way heat flows on a curved surfa ce. For a short time\, the heat diffusion will be much the same\, but soon the geometry of the surface will play a role. For example\, if the surfac e has sharp corners\, this can create irregularities in the heat flow. If the surface is smooth and closed\, like a ball\, the heat will eventually travel back around to create complex interactions with itself\, converging to an equilibrium of uniformly positive heat everywhere.\n\nIt turns out that the evolution of heat in a space is exactly related to the way a part icle randomly diffuses in that space subject to its geometry\, in the sens e that the probability that a random particle released from some initial p oint later finds itself inside some subset is exactly the proportion of he at in that subset from a unit of heat applied to the same initial point. A s suggested above\, nice properties of the geometry give rise to regularit y properties of these probabilities. More particularly\, in finite dimensi ons\, "hypoellipticity" is a standard assumption required for regularity. Analogous regularity properties in infinite dimensions have allowed the de velopment of a calculus that has become an invaluable tool in the analysis of random processes and their applications. However\, in infinite dimensi ons it has remained elusive to demonstrate that hypoellipticity is a suffi cient condition for regularity. We will discuss some infinite-dimensional model spaces where there have been positive results.\n\nIn addition to bei ng accessible on Zoom\, the talk will be projected in Jones 301.\n LOCATION:https://researchseminars.org/talk/WMmathcolloq/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ming-Jun Lai (University of Georgia) DTSTART:20220311T190000Z DTEND:20220311T200000Z DTSTAMP:20260422T212927Z UID:WMmathcolloq/6 DESCRIPTION:Title: A Multivariate Spline based Collocation Method for Numerical Solution of PDEs\nby Ming-Jun Lai (University of Georgia) as part of William & Mary Mathematics Colloquium\n\n\nAbstract\nThis talk is based on joint wo rk with Jinsil Lee. In this work\, we propose a collocation method based o n multivariate polynomial splines over triangulation/tetrahedralization fo r the numerical solution of partial differential equations. We start with a detailed explanation of the method for the Poisson equation and then ext end the study to the second-order elliptic PDE in non-divergence form. We shall show that the numerical solution can approximate the exact PDE solut ion very well under the assumption that the solution $u$ is in $H^3(\\Omeg a)$ over the domain $\\Omega$ which is of uniformly positive reach. Then w e present a large amount of numerical experimental results to demonstrate the performance of the method over the 2D and 3D settings. In addition\, w e present a comparison with the existing multivariate spline methods to sh ow that the newly proposed method produces a similar and sometimes more ac curate approximation in a more efficient fashion.\n LOCATION:https://researchseminars.org/talk/WMmathcolloq/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Jing Wang (University of Illinois Chicago) DTSTART:20220422T180000Z DTEND:20220422T190000Z DTSTAMP:20260422T212927Z UID:WMmathcolloq/7 DESCRIPTION:by Jing Wang (University of Illinois Chicago) as part of Willi am & Mary Mathematics Colloquium\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/WMmathcolloq/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Yehua Li (UC Riverside) DTSTART:20220429T180000Z DTEND:20220429T190000Z DTSTAMP:20260422T212927Z UID:WMmathcolloq/8 DESCRIPTION:by Yehua Li (UC Riverside) as part of William & Mary Mathemati cs Colloquium\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/WMmathcolloq/8/ END:VEVENT END:VCALENDAR