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:20260404T095121Z 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 Langlands program\, first formulated by Robert Langlands in the 1960s and since much developed and refined\, is a web of widespread conjectures tha t lie in deep theories of mathematical symmetry\, it gives schematic direc tion to navigate between a dizzying array of subfields of mathematics\, in cluding number theory\, representation theory\, algebraic geometry\, and h armonic analysis\nIn this talk\, we will explore some of these objects and connections and introduce the L-Functions and modular forms database (LMF DB) at https://www.lmfdb.org/\, as on e of its goals is to provide a compelling visualization for the connection s predicted by the Langlands program.\nFor example\, we will see how the R iemann hypothesis\, Goldbach's conjecture\, and Fermat's last theorem are related.\n LOCATION:https://stable.researchseminars.org/talk/WMmathcolloq/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Herbert Chang (University of Southern California) DTSTART:20220225T190000Z DTEND:20220225T200000Z DTSTAMP:20260404T095121Z UID:WMmathcolloq/2 DESCRIPTION:Title: Fields Medals Are Concentrated in Mathematical ‘Families’< /a>\nby Herbert Chang (University of Southern California) as part of Willi am & Mary Mathematics Colloquium\n\n\nAbstract\nThe Fields Medal\, often r eferred as the Nobel Prize of mathematics\, is awarded to no more than fou r mathematicians under the age of 40\, every 4 years. In recent years\, it s conferral has come under scrutiny of math historians\, for rewarding the existing elite rather than its original goal of elevating under-represent ed mathematicians. Prior studies of elitism focus on citational practices while characterization of the structural forces that prevent access remain unclear. Here we show the flow of elite mathematicians between countries and lingo-ethnic identity\, using network analysis and natural language pr ocessing on 240\,000 mathematicians and their advisor–advisee relationsh ips. We present quantitative evidence of how the Fields Medal helped integ rate Japan 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-represent ed at the elite level. Our results demonstrate concerted efforts by academ ic committees\, such as prize giving\, can either reinforce the existing e lite or reshape its definition. We anticipate our methodology of academic genealogical analysis can serve as a useful diagnostic for equity and syst emic bias within academic fields. The presentation will also briefly discu ss the similar use of network science and graph theory in profiling misinf ormation during the Covid-19 pandemic.\n LOCATION:https://stable.researchseminars.org/talk/WMmathcolloq/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Dana P. Williams (Dartmouth College) DTSTART:20220304T190000Z DTEND:20220304T200000Z DTSTAMP:20260404T095121Z UID:WMmathcolloq/3 DESCRIPTION:Title: The Equivalence Theorem for groupoid C*-algebras\nby Dana P. Williams (Dartmouth College) as part of William & Mary Mathematics Coll oquium\n\n\nAbstract\nOne of the original motivations for the study of C*- algebras came from noncommutative harmonic analysis and the group C*-algeb ra construction. Nowadays the representation theory of C*-algebras is an interesting subject onto itself. An essential tool is the notion of Morit a equivalence of C*-algebras which is a good deal coarser than isomorphism \, but still implies an equivalence of the representation theory. There a re many ways to build C*-algebras mimicing the group C*-algebra constructi on and a key player is the construction of C*-algebras from groupoids. So me time ago\, Jean Renault observed that a notion of groupoid equivalence implied Morita equivalence of the corresponding C*-algebras which gives a very concrete and topological way to establish deep analytic facts. After briefly outlining the necessary background\, I will give a sketch of this Equivalence Theorem using a newer proof developed by Aidan Sims and mysel f.\n LOCATION:https://stable.researchseminars.org/talk/WMmathcolloq/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Mahlet Tadesse (Georgetown University) DTSTART:20220325T180000Z DTEND:20220325T190000Z DTSTAMP:20260404T095121Z UID:WMmathcolloq/4 DESCRIPTION:Title: Uncovering cluster structures and relevant biomarkers in “-o mics” data\nby Mahlet Tadesse (Georgetown University) as part of Wil liam & Mary Mathematics Colloquium\n\n\nAbstract\nHigh-throughput “-omic s” technologies (genomics\, epigenomics\, transcriptomics\, proteomics\, metabolomics\, etc) allow the simultaneous quantification of thousands of biomarkers. These technologies hold great potential for gaining insights into the complex biological processes underlying specific phenotypes and f or identifying biomarkers that can be used for improved diagnosis and ther apeutic interventions. The challenges of analyzing the generated data have led to the development of various statistical\, computational and bioinfo rmatic tools over the the past couple of decades. In this talk\, I will pr esent some of the methods we have proposed for uncovering cluster structur es and relevant biomarkers by combining ideas of mixture models and variab le selection. I will discuss (1) a bi-clustering approach that allows clus tering on subsets of variables to refine disease classes and identify disc riminating biomarkers\, (2) an integrative model to relate data from diffe rent -omic levels using a stochastic partitioning method\, and (3) a mixtu re of regression trees approach to uncover homogeneous disease subgroups a nd their associated predictors accounting for non-linear relationships and interaction effects. I will illustrate the methods on various -omic studi es.\n LOCATION:https://stable.researchseminars.org/talk/WMmathcolloq/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Tai Melcher (University of Virginia) DTSTART:20220408T180000Z DTEND:20220408T190000Z DTSTAMP:20260404T095121Z UID:WMmathcolloq/5 DESCRIPTION:Title: Hypoellipticity in infinite dimensions\nby Tai Melcher (Un iversity of Virginia) as part of William & Mary Mathematics Colloquium\n\n \nAbstract\nConsider a flat infinite surface to which one applies a unit o f heat at a fixed point and then steps away allowing the heat to propagate . The heat flows quickly at first and then ever more slowly as it converge s everywhere to zero. Contrast this now with the way heat flows on a curve d surface. For a short time\, the heat diffusion will be much the same\, b ut soon the geometry of the surface will play a role. For example\, if the surface has sharp corners\, this can create irregularities in the heat fl ow. If the surface is smooth and closed\, like a ball\, the heat will even tually travel back around to create complex interactions with itself\, con verging to an equilibrium of uniformly positive heat everywhere.\n\nIt tur ns out that the evolution of heat in a space is exactly related to the way a particle randomly diffuses in that space subject to its geometry\, in t he sense that the probability that a random particle released from some in itial point later finds itself inside some subset is exactly the proportio n of heat in that subset from a unit of heat applied to the same initial p oint. As suggested above\, nice properties of the geometry give rise to re gularity properties of these probabilities. More particularly\, in finite dimensions\, "hypoellipticity" is a standard assumption required for regul arity. Analogous regularity properties in infinite dimensions have allowed the development of a calculus that has become an invaluable tool in the a nalysis of random processes and their applications. However\, in infinite dimensions it has remained elusive to demonstrate that hypoellipticity is a sufficient condition for regularity. We will discuss some infinite-dimen sional model spaces where there have been positive results.\n\nIn addition to being accessible on Zoom\, the talk will be projected in Jones 301.\n LOCATION:https://stable.researchseminars.org/talk/WMmathcolloq/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ming-Jun Lai (University of Georgia) DTSTART:20220311T190000Z DTEND:20220311T200000Z DTSTAMP:20260404T095121Z UID:WMmathcolloq/6 DESCRIPTION:Title: A Multivariate Spline based Collocation Method for Numerical S olution of PDEs\nby Ming-Jun Lai (University of Georgia) as part of Wi lliam & Mary Mathematics Colloquium\n\n\nAbstract\nThis talk is based on j oint work with Jinsil Lee. In this work\, we propose a collocation method based on multivariate polynomial splines over triangulation/tetrahedraliza tion for the numerical solution of partial differential equations. We star t with a detailed explanation of the method for the Poisson equation and t hen extend the study to the second-order elliptic PDE in non-divergence fo rm. We shall show that the numerical solution can approximate the exact PD E solution very well under the assumption that the solution $u$ is in $H^3 (\\Omega)$ over the domain $\\Omega$ which is of uniformly positive reach. Then we present a large amount of numerical experimental results to demon strate the performance of the method over the 2D and 3D settings. In addit ion\, we present a comparison with the existing multivariate spline method s to show that the newly proposed method produces a similar and sometimes more accurate approximation in a more efficient fashion.\n LOCATION:https://stable.researchseminars.org/talk/WMmathcolloq/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Jing Wang (University of Illinois Chicago) DTSTART:20220422T180000Z DTEND:20220422T190000Z DTSTAMP:20260404T095121Z 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://stable.researchseminars.org/talk/WMmathcolloq/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Yehua Li (UC Riverside) DTSTART:20220429T180000Z DTEND:20220429T190000Z DTSTAMP:20260404T095121Z UID:WMmathcolloq/8 DESCRIPTION:by Yehua Li (UC Riverside) as part of William & Mary Mathemati cs Colloquium\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/WMmathcolloq/8/ END:VEVENT END:VCALENDAR