BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lillian Pierce (Duke University) DTSTART;VALUE=DATE-TIME:20210211T203000Z DTEND;VALUE=DATE-TIME:20210211T213000Z DTSTAMP;VALUE=DATE-TIME:20211022T090530Z UID:1123112229/1 DESCRIPTION:Title: Counting problems: open questions in number theory\, from the perspecti ve of moments\nby Lillian Pierce (Duke University) as part of K-State Mathematics Department Women Lecture Series\n\n\nAbstract\nMany questions in number theory can be phrased as counting problems. How many number fiel ds are there? How many elliptic curves are there? How many integral soluti ons to this system of Diophantine equations are there? If the answer is “infinitely many\,” we want to understand the order of growth for the number of objects we are counting in the “family." But in many settings we are also interested in finer-grained questions\, like: how many number fields are there\, with fixed degree and fixed discriminant? We know the a nswer is “finitely many\,” but it would have important consequences if we could show the answer is always “very few indeed.” In this accessi ble talk\, we will describe a way that these finer-grained questions can b e related to the bigger infinite-family questions. Then we will use this p erspective to survey interconnections between several big open conjectures in number theory\, related in particular to class groups and number field s.\n LOCATION:https://researchseminars.org/talk/1123112229/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Yu-Ru Liu (University of Waterloo) DTSTART;VALUE=DATE-TIME:20210223T203000Z DTEND;VALUE=DATE-TIME:20210223T213000Z DTSTAMP;VALUE=DATE-TIME:20211022T090530Z UID:1123112229/2 DESCRIPTION:Title: Diophantine Problems in Function Fields\nby Yu-Ru Liu (University o f Waterloo) as part of K-State Mathematics Department Women Lecture Series \n\n\nAbstract\nLet $\\mathbb{Z}$ be the ring of integers\, and let $\\mat hbb{F}_p[t]$ be the ring of polynomials in one variable defined over the f inite field $\\mathbb{F}_p$ of $p$ elements. Since the characteristic of $\\mathbb{Z}$ is $0$\, while that of $\\mathbb{F}_p[t]$ is the positive pri me number $p$\, it is an interesting phenomenon in arithmetic that these t wo rings resemble one another so faithfully. The study of the similarity a nd difference between $\\mathbb{Z}$ and $\\mathbb{F}_p[t]$ lies in the fie ld that relates number fields to function fields. In this talk\, we will i nvestigate some Diophantine problems in the settings of $\\mathbb{Z}$ and $\\mathbb{F}_p[t]$\, including Waring's problem about representations of elements with fixed powers.\n LOCATION:https://researchseminars.org/talk/1123112229/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Svitlana Mayboroada (University of Minnesota) DTSTART;VALUE=DATE-TIME:20210311T203000Z DTEND;VALUE=DATE-TIME:20210311T213000Z DTSTAMP;VALUE=DATE-TIME:20211022T090530Z UID:1123112229/3 DESCRIPTION:Title: The hidden landscape of wave localization\nby Svitlana Mayboroada ( University of Minnesota) as part of K-State Mathematics Department Women L ecture Series\n\n\nAbstract\nComplexity of the geometry\, randomness of th e potential\, and many other irregularities of the system can cause powerf ul\, albeit quite different\, manifestations of localization\, a phenomeno n of sudden confinement of waves to a small portion of the original domain . In the present talk we show that behind a possibly disordered system the re exists a structure\, referred to as a landscape function\, which predic ts the location and shape of the localized waves\, a pattern of their deca y\, and delivers accurate bounds for the corresponding energies.\n LOCATION:https://researchseminars.org/talk/1123112229/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Irene Fonseca (Carnegie Melon University) DTSTART;VALUE=DATE-TIME:20210422T193000Z DTEND;VALUE=DATE-TIME:20210422T203000Z DTSTAMP;VALUE=DATE-TIME:20211022T090530Z UID:1123112229/4 DESCRIPTION:Title: Phase transitions in heterogeneous media: equilibria and geometric flow s\nby Irene Fonseca (Carnegie Melon University) as part of K-State Mat hematics Department Women Lecture Series\n\n\nAbstract\nA variational mode l in the context of the gradient theory for fluid-fluid phase transitions with small scale heterogeneities is studied. In the case where the scale o f the small homogeneities is of the same order of the scale governing the phase transition\, the interaction between homogenization and the phase tr ansitions process leads to an anisotropic interfacial energy.\n\nThe under lying gradient flow provides unconditional convergence results for an Alle n-Cahn type bi-stable reaction diffusion equation in a periodic medium. Th e limiting dynamics are given by an analog for anisotropic mean curvature flow\, of the formulation due to Ken Brakke. As an essential ingredient in the analysis\, an explicit expression for the effective surface tension\, which dictates the limiting anisotropic mean curvature\, is obtained.\n\n This is joint work with Riccardo Cristoferi (Radboud University\, The Neth erlands)\, Adrian Hagerty\, Cristina Popovici\, Rustum Choksi (McGill)\, J essica Lin (McGill)\, and Raghavendra Venkatraman (CMU).\n LOCATION:https://researchseminars.org/talk/1123112229/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Betsy Stovall (University of Wisconsin) DTSTART;VALUE=DATE-TIME:20210330T193000Z DTEND;VALUE=DATE-TIME:20210330T203000Z DTSTAMP;VALUE=DATE-TIME:20211022T090530Z UID:1123112229/5 DESCRIPTION:Title: Maximizers and near-maximizers for Fourier restriction inequalities \nby Betsy Stovall (University of Wisconsin) as part of K-State Mathematic s Department Women Lecture Series\n\n\nAbstract\nFourier restriction pheno mena allow us to make sense out of the restriction of the Fourier transfor m of an $L^p$ function (nominally only defined almost everywhere) on measu re zero sets\, provided these sets possess sufficient curvature. In the d ual formulation\, "tubes" whose directions are restricted to lie along som e curved set can only overlap with one another on a relatively small regio n of space. More quantitatively\, such phenomena are reflected by Lebesgu e space bounds for the Fourier restriction operator. In this talk\, we wi ll describe some open questions and recent results regarding the existence of functions that provide a worst-case scenario by saturating these Lebes gue space bounds.\n LOCATION:https://researchseminars.org/talk/1123112229/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Blair Sullivan (University of Utah) DTSTART;VALUE=DATE-TIME:20210506T193000Z DTEND;VALUE=DATE-TIME:20210506T203000Z DTSTAMP;VALUE=DATE-TIME:20211022T090530Z UID:1123112229/6 DESCRIPTION:Title: Putting parameterization into practice\nby Blair Sullivan (Universi ty of Utah) as part of K-State Mathematics Department Women Lecture Series \n\n\nAbstract\nThe field of network science has burgeoned in the last two decades\, developing new methods for analyzing complex network data of ev er-increasing scale. Surprisingly\, few approaches draw on the wealth of e fficient algorithms arising from structural graph theory and parameterized complexity. In part\, this is due to the primarily theoretical nature of the related literature\, unrealistic structural assumptions\, and a lack o f cross-pollination of the research communities. In this talk\, we survey the key ingredients for bridging this theory-practice gap\, and describe s everal applications which demonstrate the potential of parameterized graph algorithms in computational genomics.\n LOCATION:https://researchseminars.org/talk/1123112229/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Riehl (Johns Hopkins University) DTSTART;VALUE=DATE-TIME:20210916T193000Z DTEND;VALUE=DATE-TIME:20210916T203000Z DTSTAMP;VALUE=DATE-TIME:20211022T090530Z UID:1123112229/7 DESCRIPTION:Title: Contractibility as uniqueness\nby Emily Riehl (Johns Hopkins Unive rsity) as part of K-State Mathematics Department Women Lecture Series\n\n\ nAbstract\nWhat does it mean for something to exist uniquely? Classically\ , to say that a set A has a unique element means that there is an element x of A and any other element y of A equals x. When this assertion is appli ed to a space A\, instead of a mere set\, and interpreted in a continuous fashion\, it encodes the statement that the space is contractible\, i.e.\, that A is continuously deformable to a point. This talk will explore this notion of contractibility as uniqueness and its role in generalizing from ordinary categories to infinite-dimensional categories.\n LOCATION:https://researchseminars.org/talk/1123112229/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Jennifer Balakrishnan (Boston University) DTSTART;VALUE=DATE-TIME:20210928T193000Z DTEND;VALUE=DATE-TIME:20210928T203000Z DTSTAMP;VALUE=DATE-TIME:20211022T090530Z UID:1123112229/8 DESCRIPTION:Title: Questions about rational points on curves\nby Jennifer Balakrishnan (Boston University) as part of K-State Mathematics Department Women Lectu re Series\n\n\nAbstract\nA rational point on a curve is a point whose coor dinates are both rational numbers. When a curve has genus 2 or more\, by a theorem of Faltings\, there are always only finitely many rational points . Yet many more questions remain: how many rational points are there exact ly? Is there an algorithm to find them all? I'll discuss these questions a nd more (ranging from the time of the ancient Greeks to the present)\, off er some answers\, and highlight a selection of illustrative examples.\n LOCATION:https://researchseminars.org/talk/1123112229/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Juanita Pinzón Caicedo (University of Notre Dame) DTSTART;VALUE=DATE-TIME:20211014T193000Z DTEND;VALUE=DATE-TIME:20211014T202000Z DTSTAMP;VALUE=DATE-TIME:20211022T090530Z UID:1123112229/9 DESCRIPTION:Title: Instantons and knot concordance\nby Juanita Pinzón Caicedo (Univer sity of Notre Dame) as part of K-State Mathematics Department Women Lectur e Series\n\nLecture held in Room 122 in Cardwell Hall.\n\nAbstract\nKnot c oncordance can be regarded as the study of knots as boundaries of surfaces embedded in spaces of dimension 4. Specifically\, two knots $K_0$ and $K_ 1$ are said to be smoothly concordant if there is a smooth embedding of th e annulus $S^1 \\times [0\, 1]$ into the “cylinder” $S^3 \\times [0\, 1]$ that restricts to the given knots at each end. Smooth concordance is a n equivalence relation\, and the set C of smooth concordance classes of kn ots is an abelian group with connected sum as the binary operation. The al gebraic structure of $C$\, the concordance class of the unknot\, and the s et of knots that are topologically slice but not smoothly slice are much s tudied objects in low-dimensional topology. Gauge theoretical results on t he nonexistence of certain definite smooth 4-manifolds can be used to bett er understand these objects. In particular\, the study of anti-self dual c onnections on 4-manifolds can be used to shown that the group of topologic ally slice knots up to smooth concordance contains a subgroup isomorphic t o $Z^\\infty.$\n LOCATION:https://researchseminars.org/talk/1123112229/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Sara Billey (University of Washington) DTSTART;VALUE=DATE-TIME:20211028T193000Z DTEND;VALUE=DATE-TIME:20211028T202000Z DTSTAMP;VALUE=DATE-TIME:20211022T090530Z UID:1123112229/10 DESCRIPTION:Title: Some Theorems in Asymptotic Algebraic Combinatorics\nby Sara Bille y (University of Washington) as part of K-State Mathematics Department Wom en Lecture Series\n\nInteractive livestream: https://youtu.be/kOgzewZY8_M\ n\nAbstract\nAsymptotic Combinatorics is a branch of Mathematics that look s at limiting distributions of combinatorial formulas. Our recent work ha s focused on generalizations of a classic formula for standard Young table aux called the Hook Length Formula and its generalizations to using the ma jor index statistic. Further examples include Stanley’s q-hook-content formula for semistandard tableaux and q-hook length formulas of Björner –Wachs related to linear extensions of labeled forests. We show that\, w hile these limiting distributions are “generically” asymptotically nor mal\, there are uncountably many non-normal limit laws. More precisely\, w e introduce and completely describe the compact closure of the moduli spac e of distributions of these statistics in several regimes. The additional limit distributions involve generalized uniform sum distributions which ar e topologically parameterized by certain decreasing sequence spaces with b ounded 2-norm. The closure of the moduli space of these distributions in t he Lévy metric gives rise to the moduli space of DUSTPAN distributions. A s an application\, we completely classify the limiting distributions of th e size statistic on plane partitions fitting in a box. This talk is based on joint work with Joshua Swanson at USC (https://arxiv.org/abs/2010.12701 ).\n LOCATION:https://researchseminars.org/talk/1123112229/10/ URL:https://youtu.be/kOgzewZY8_M END:VEVENT END:VCALENDAR