BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lillian Pierce (Duke University) DTSTART:20210211T203000Z DTEND:20210211T213000Z DTSTAMP:20260404T111416Z UID:1123112229/1 DESCRIPTION:Title: Counting problems: open questions in number theory\, from the pe rspective of moments\nby Lillian Pierce (Duke University) as part of K -State Mathematics Department Women Lecture Series\n\n\nAbstract\nMany que stions in number theory can be phrased as counting problems. How many numb er fields are there? How many elliptic curves are there? How many integral solutions to this system of Diophantine equations are there? If the answe r 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 sett ings we are also interested in finer-grained questions\, like: how many nu mber fields are there\, with fixed degree and fixed discriminant? We know the answer is “finitely many\,” but it would have important consequenc es if we could show the answer is always “very few indeed.” In this ac cessible talk\, we will describe a way that these finer-grained questions can be related to the bigger infinite-family questions. Then we will use t his perspective to survey interconnections between several big open conjec tures in number theory\, related in particular to class groups and number fields.\n LOCATION:https://stable.researchseminars.org/talk/1123112229/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Yu-Ru Liu (University of Waterloo) DTSTART:20210223T203000Z DTEND:20210223T213000Z DTSTAMP:20260404T111416Z UID:1123112229/2 DESCRIPTION:Title: Diophantine Problems in Function Fields\nby Yu-Ru Liu (Unive rsity of Waterloo) as part of K-State Mathematics Department Women Lecture Series\n\n\nAbstract\nLet $\\mathbb{Z}$ be the ring of integers\, and let $\\mathbb{F}_p[t]$ be the ring of polynomials in one variable defined ove r the finite field $\\mathbb{F}_p$ of $p$ elements. Since the characterist ic of $\\mathbb{Z}$ is $0$\, while that of $\\mathbb{F}_p[t]$ is the posit ive prime number $p$\, it is an interesting phenomenon in arithmetic that these two rings resemble one another so faithfully. The study of the simil arity and difference between $\\mathbb{Z}$ and $\\mathbb{F}_p[t]$ lies in the field that relates number fields to function fields. In this talk\, we will investigate some Diophantine problems in the settings of $\\mathbb{ Z}$ and $\\mathbb{F}_p[t]$\, including Waring's problem about representati ons of elements with fixed powers.\n LOCATION:https://stable.researchseminars.org/talk/1123112229/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Svitlana Mayboroada (University of Minnesota) DTSTART:20210311T203000Z DTEND:20210311T213000Z DTSTAMP:20260404T111416Z UID:1123112229/3 DESCRIPTION:Title: The hidden landscape of wave localization\nby Svitlana Maybo roada (University of Minnesota) as part of K-State Mathematics Department Women Lecture Series\n\n\nAbstract\nComplexity of the geometry\, randomnes s of the potential\, and many other irregularities of the system can cause powerful\, albeit quite different\, manifestations of localization\, a ph enomenon of sudden confinement of waves to a small portion of the original domain. In the present talk we show that behind a possibly disordered sys tem there exists a structure\, referred to as a landscape function\, which predicts the location and shape of the localized waves\, a pattern of the ir decay\, and delivers accurate bounds for the corresponding energies.\n LOCATION:https://stable.researchseminars.org/talk/1123112229/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Irene Fonseca (Carnegie Melon University) DTSTART:20210422T193000Z DTEND:20210422T203000Z DTSTAMP:20260404T111416Z UID:1123112229/4 DESCRIPTION:Title: Phase transitions in heterogeneous media: equilibria and geometr ic flows\nby Irene Fonseca (Carnegie Melon University) as part of K-St ate Mathematics Department Women Lecture Series\n\n\nAbstract\nA variation al model in the context of the gradient theory for fluid-fluid phase trans itions with small scale heterogeneities is studied. In the case where the scale of the small homogeneities is of the same order of the scale governi ng the phase transition\, the interaction between homogenization and the p hase transitions process leads to an anisotropic interfacial energy.\n\nTh e underlying gradient flow provides unconditional convergence results for an Allen-Cahn type bi-stable reaction diffusion equation in a periodic med ium. The limiting dynamics are given by an analog for anisotropic mean cur vature flow\, of the formulation due to Ken Brakke. As an essential ingred ient in the analysis\, an explicit expression for the effective surface te nsion\, which dictates the limiting anisotropic mean curvature\, is obtain ed.\n\nThis is joint work with Riccardo Cristoferi (Radboud University\, T he Netherlands)\, Adrian Hagerty\, Cristina Popovici\, Rustum Choksi (McGi ll)\, Jessica Lin (McGill)\, and Raghavendra Venkatraman (CMU).\n LOCATION:https://stable.researchseminars.org/talk/1123112229/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Betsy Stovall (University of Wisconsin) DTSTART:20210330T193000Z DTEND:20210330T203000Z DTSTAMP:20260404T111416Z UID:1123112229/5 DESCRIPTION:Title: Maximizers and near-maximizers for Fourier restriction inequalit ies\nby Betsy Stovall (University of Wisconsin) as part of K-State Mat hematics Department Women Lecture Series\n\n\nAbstract\nFourier restrictio n phenomena allow us to make sense out of the restriction of the Fourier t ransform of an $L^p$ function (nominally only defined almost everywhere) o n measure zero sets\, provided these sets possess sufficient curvature. I n the dual formulation\, "tubes" whose directions are restricted to lie al ong some curved set can only overlap with one another on a relatively smal l region of space. More quantitatively\, such phenomena are reflected by Lebesgue space bounds for the Fourier restriction operator. In this talk\ , we will describe some open questions and recent results regarding the ex istence of functions that provide a worst-case scenario by saturating thes e Lebesgue space bounds.\n LOCATION:https://stable.researchseminars.org/talk/1123112229/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Blair Sullivan (University of Utah) DTSTART:20210506T193000Z DTEND:20210506T203000Z DTSTAMP:20260404T111416Z UID:1123112229/6 DESCRIPTION:Title: Putting parameterization into practice\nby Blair Sullivan (U niversity of Utah) as part of K-State Mathematics Department Women Lecture Series\n\n\nAbstract\nThe field of network science has burgeoned in the l ast two decades\, developing new methods for analyzing complex network dat a of ever-increasing scale. Surprisingly\, few approaches draw on the weal th of efficient algorithms arising from structural graph theory and parame terized complexity. In part\, this is due to the primarily theoretical nat ure of the related literature\, unrealistic structural assumptions\, and a lack of cross-pollination of the research communities. In this talk\, we survey the key ingredients for bridging this theory-practice gap\, and des cribe several applications which demonstrate the potential of parameterize d graph algorithms in computational genomics.\n LOCATION:https://stable.researchseminars.org/talk/1123112229/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Riehl (Johns Hopkins University) DTSTART:20210916T193000Z DTEND:20210916T203000Z DTSTAMP:20260404T111416Z UID:1123112229/7 DESCRIPTION:Title: Contractibility as uniqueness\nby Emily Riehl (Johns Hopkin s University) as part of K-State Mathematics Department Women Lecture Seri es\n\n\nAbstract\nWhat does it mean for something to exist uniquely? Class ically\, to say that a set A has a unique element means that there is an e lement x of A and any other element y of A equals x. When this assertion i s applied to a space A\, instead of a mere set\, and interpreted in a cont inuous fashion\, it encodes the statement that the space is contractible\, i.e.\, that A is continuously deformable to a point. This talk will explo re this notion of contractibility as uniqueness and its role in generalizi ng from ordinary categories to infinite-dimensional categories.\n LOCATION:https://stable.researchseminars.org/talk/1123112229/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Jennifer Balakrishnan (Boston University) DTSTART:20210928T193000Z DTEND:20210928T203000Z DTSTAMP:20260404T111416Z UID:1123112229/8 DESCRIPTION:Title: Questions about rational points on curves\nby Jennifer Balak rishnan (Boston University) as part of K-State Mathematics Department Wome n Lecture Series\n\n\nAbstract\nA rational point on a curve is a point who se coordinates 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 ther e exactly? Is there an algorithm to find them all? I'll discuss these ques tions and more (ranging from the time of the ancient Greeks to the present )\, offer some answers\, and highlight a selection of illustrative example s.\n LOCATION:https://stable.researchseminars.org/talk/1123112229/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Juanita Pinzón Caicedo (University of Notre Dame) DTSTART:20211014T193000Z DTEND:20211014T202000Z DTSTAMP:20260404T111416Z UID:1123112229/9 DESCRIPTION:Title: Instantons and knot concordance\nby Juanita Pinzón Caicedo (University of Notre Dame) as part of K-State Mathematics Department Women Lecture Series\n\nLecture held in Room 122 in Cardwell Hall.\n\nAbstract\ nKnot concordance can be regarded as the study of knots as boundaries of s urfaces 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 embeddin g of the annulus $S^1 \\times [0\, 1]$ into the “cylinder” $S^3 \\time s [0\, 1]$ that restricts to the given knots at each end. Smooth concordan ce is an equivalence relation\, and the set C of smooth concordance classe s of knots is an abelian group with connected sum as the binary operation. The algebraic structure of $C$\, the concordance class of the unknot\, an d the set of knots that are topologically slice but not smoothly slice are much studied objects in low-dimensional topology. Gauge theoretical resul ts on the nonexistence of certain definite smooth 4-manifolds can be used to better understand these objects. In particular\, the study of anti-self dual connections on 4-manifolds can be used to shown that the group of to pologically slice knots up to smooth concordance contains a subgroup isomo rphic to $Z^\\infty.$\n LOCATION:https://stable.researchseminars.org/talk/1123112229/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Sara Billey (University of Washington) DTSTART:20211028T193000Z DTEND:20211028T202000Z DTSTAMP:20260404T111416Z UID:1123112229/10 DESCRIPTION:Title: Some Theorems in Asymptotic Algebraic Combinatorics\nby Sar a Billey (University of Washington) as part of K-State Mathematics Departm ent Women Lecture Series\n\n\nAbstract\nAsymptotic Combinatorics is a bran ch of Mathematics that looks at limiting distributions of combinatorial fo rmulas. Our recent work has focused on generalizations of a classic formu la for standard Young tableaux called the Hook Length Formula and its gene ralizations to using the major index statistic. Further examples include Stanley’s q-hook-content formula for semistandard tableaux and q-hook le ngth formulas of Björner–Wachs related to linear extensions of labeled forests. We show that\, while these limiting distributions are “generica lly” asymptotically normal\, there are uncountably many non-normal limit laws. More precisely\, we introduce and completely describe the compact c losure of the moduli space of distributions of these statistics in several regimes. The additional limit distributions involve generalized uniform s um distributions which are topologically parameterized by certain decreasi ng sequence spaces with bounded 2-norm. The closure of the moduli space of these distributions in the Lévy metric gives rise to the moduli space of DUSTPAN distributions. As an application\, we completely classify the lim iting distributions of the 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://stable.researchseminars.org/talk/1123112229/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Nageswari Shanmugalingam (University of Cincinnati) DTSTART:20211118T203000Z DTEND:20211118T212000Z DTSTAMP:20260404T111416Z UID:1123112229/11 DESCRIPTION:Title: A multitude of formulations of Dirichlet problem for least grad ient functional\nby Nageswari Shanmugalingam (University of Cincinnati ) as part of K-State Mathematics Department Women Lecture Series\n\nLectur e held in Cardwell 101.\n\nAbstract\nWe are always trying to optimize thin gs in practice: taking the shortest path\, maximizing productivity\, minim izing energy spent. A class of elliptic PDEs would have us minimizing ener gy. For example\, when $1 < p < \\infty$\, minimizing the energy $\\int_\\ Omega |\\nabla u|^p d\\mu$ subject to some boundary constraint is equivale nt to solving the problem $-\\Delta_p u=0$ in $\\Omega$ with Dirichlet bou ndary data. Solutions to this problem are now relatively well-understood. When $p=1$\, the minimization problem becomes purely geometric\, and is re lated to minimal surfaces. However\, the corresponding Dirichlet type cond ition can fail for this problem. We will discuss various ways of re-formul ating the Dirichlet problem to obtain reasonable solutions\, even in weigh ted Euclidean settings.\n LOCATION:https://stable.researchseminars.org/talk/1123112229/11/ END:VEVENT END:VCALENDAR