BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Stella Sue Gastineau (Boston College) DTSTART:20200520T220000Z DTEND:20200520T230000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/1 DESCRIPTION:Title: Diving into the shallow end\nby Stella Sue Gastineau (Boston College) as part of University of Oregon Number Theory Seminar\n\n\nAbstra ct\nIn 2013\, Reeder-Yu gave a construction of supercuspidal representatio ns by starting with stable characters coming from the shallowest depth of the Moy-Prasad filtration. In this talk\, we will be diving deeper—but n ot too deep. In doing so\, we will construct examples of supercuspidal rep resentations coming from a larger class of "shallow" characters. Using met hods similar to Reeder-Yu\, we can begin to make predictions about the Lan glands parameters for these representations.\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Chi-Yun Hsu (University of California\, Los Angeles) DTSTART:20200527T220000Z DTEND:20200527T230000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/2 DESCRIPTION:Title: Construction of Euler Systems for $\\mathrm{GSp}_4×\\mathrm{GL}_ 2$\nby Chi-Yun Hsu (University of California\, Los Angeles) as part of University of Oregon Number Theory Seminar\n\n\nAbstract\nAn Euler system is a collection of norm-compatible first Galois cohomology classes with t he Galois groups varying over cyclotomic fields. By constructing an Euler system\, one can bound the Selmer group of Galois representations. We cons truct Euler systems for the Galois representations coming from automorphic representations of $\\mathrm{GSp}_4×\\mathrm{GL}_2$. The strategy follow s the work of Loeffler-Zerbes-Skinner in the case of $\\mathrm{GSp}_4$\, u sing automorphic input to show norm compatibility. This is a work in progr ess with Zhaorong Jin and Ryotaro Sakamoto.\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Christelle Vincent (University of Vermont) DTSTART:20200603T220000Z DTEND:20200603T230000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/3 DESCRIPTION:Title: On the equidistribution of joint shapes of rings and their resolv ents\nby Christelle Vincent (University of Vermont) as part of Univers ity of Oregon Number Theory Seminar\n\n\nAbstract\nIn her thesis\, Piper H showed that "shapes of number fields" are "equidistributed" under certain mild and expected conditions. The proof uses Bhargava's parametrization o f cubic\, quartic\, and quintic rings\, which itself works by attaching to each such ring one or more "resolvent ring" and parametrizing rings with a choice of resolvent.\n\nA natural question then arises: Are the shapes o f a ring and its resolvent independent of one another\; in other words is the ordered pair of shapes equidistributed too? What if we replace rings a nd a choice of resolvent ring with fields and their resolvent fields?\n\nI n this talk we will introduce the notion of the shape of a ring or number field\, briefly define what we mean by equidistribution in this context\, and describe the resolvent ring of a quartic ring. We will then give a gli mpse of the difficulties in extending a result about rings and their resol vents to fields and their resolvents. This is joint work with Piper H.\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Joe Webster (University of Oregon) DTSTART:20201021T180000Z DTEND:20201021T190000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/4 DESCRIPTION:Title: The p-adic Mehta Integral\nby Joe Webster (University of Oreg on) as part of University of Oregon Number Theory Seminar\n\n\nAbstract\nT he Mehta integral is the canonical partition function for 1-dimensional lo g-Coulomb gas in a harmonic potential well. Mehta and Dyson showed that it also determines the joint probability densities for the eigenvalues of Ga ussian random matrix ensembles\, and Bombieri later found its explicit for m. We introduce the p-adic analogue of the Mehta integral as the canonical partition function for a p-adic log-Coulomb gas\, discuss its underlying combinatorial structure\, and find its explicit formula and domain.\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Yujie Xu (Harvard) DTSTART:20201104T190000Z DTEND:20201104T200000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/5 DESCRIPTION:by Yujie Xu (Harvard) as part of University of Oregon Number T heory Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Mathilde Gerbelli-Gauthier (University of Chicago) DTSTART:20201111T190000Z DTEND:20201111T200000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/6 DESCRIPTION:Title: Cohomology of Arithmetic Groups and Endoscopy\nby Mathilde Ge rbelli-Gauthier (University of Chicago) as part of University of Oregon Nu mber Theory Seminar\n\n\nAbstract\nHow fast do Betti numbers grow in a con gruence tower of compact arithmetic manifolds? The dimension of the middle degree of cohomology is proportional to the volume of the manifold\, but away from the middle the growth is known to be sub-linear in the volume. I will explain how automorphic representations and the phenomenon of endosc opy provide a framework to understand and quantify this slow growth. Speci fically\, I will discuss how to obtain some explicit bounds in the case of unitary groups using Arthur's stable trace formula.\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Melissa Emory (University of Toronto) DTSTART:20201118T190000Z DTEND:20201118T200000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/7 DESCRIPTION:Title: A multiplicity one theorem for general spin groups\nby Meliss a Emory (University of Toronto) as part of University of Oregon Number The ory Seminar\n\n\nAbstract\nA classical problem in representation theory is how a\nrepresentation of a group decomposes when restricted to a subgroup . In the\n1990s\, Gross-Prasad formulated an intriguing conjecture regardi ng the\nrestriction of representations\, also known as branching laws\, of special\northogonal groups. Gan\, Gross and Prasad extended this conject ure\, now\nknown as the local Gan-Gross-Prasad (GGP) conjecture\, to the r emaining\nclassical groups. There are many ingredients needed to prove a l ocal GGP\nconjecture. In this talk\, we will focus on the first ingredien t: a\nmultiplicity at most one theorem. Aizenbud\, Gourevitch\, Rallis and \nSchiffmann proved a multiplicity (at most) one theorem for restrictions of\nirreducible representations of certain p-adic classical groups and\nWa ldspurger proved the same theorem for the special orthogonal groups. We\nw ill discuss work that establishes a multiplicity (at most) one theorem\nfo r restrictions of irreducible representations for a non-classical group\,\ nthe general spin group. This is joint work with Shuichiro Takeda.\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Jon Aycock (University of Oregon) DTSTART:20201125T190000Z DTEND:20201125T200000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/8 DESCRIPTION:Title: Overconvergent Differential Operators Acting on Modular Forms.\nby Jon Aycock (University of Oregon) as part of University of Oregon Nu mber Theory Seminar\n\n\nAbstract\nIn the 1970's\, Katz used Damerell's fo rmula to construct p-adic L-functions for CM fields by interpolating diffe rential operators. However\, these operators were only defined over the or dinary locus\, leading to restrictions on p. Recently\, a geometric theory of overconvergent modular forms has given a way around these restrictions . I will describe how to do this in the case of modular forms\, and then g ive a brief template for the Hilbert case.\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Ananth Shankar (University of Wisconsin) DTSTART:20201202T190000Z DTEND:20201202T200000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/9 DESCRIPTION:Title: A finiteness criterion for 2-dimensional representations of surfa ce groups\nby Ananth Shankar (University of Wisconsin) as part of Univ ersity of Oregon Number Theory Seminar\n\n\nAbstract\nLet C be a a complex algebraic curve of genus $\\geq 1$\, and let $\\pi$ be its fundamental gr oup. Let $\\rho: \\pi\\rightarrow \\GL_2(\\C)$ be a semisimple 2-dimension al representation\, such that $\\rho(\\alpha)$ has finite order for every simple closed loop $\\alpha.$ We will prove that $\\rho$ has finite image. If time permits\, we will mention applications of this result to the Grot hendieck-Katz p-curvature conjecture. This is joint work with Anand Patel and Junho Peter Whang.\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Ari Shnidman (Hebrew University of Jerusalem) DTSTART:20210217T190000Z DTEND:20210217T200000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/10 DESCRIPTION:Title: Rational points on twist families of curves\nby Ari Shnidman (Hebrew University of Jerusalem) as part of University of Oregon Number T heory Seminar\n\n\nAbstract\nA curve C of genus g > 1 has finite automorph ism group G. If C is defined over a number field F\, we consider a twist f amily of C\, which is a family of curves over F each of which is isomorphi c C over the algebraic closure of F. For example\, the family C_d : x^6 + y^6 = d is a family of twists of the degree 6 fermat curve C_1. In this t alk\, I'll present some results which show that for various twist families \, a large proportion of twists have very few F-rational points. For exam ple\, we can show that C_d(Q) is empty for at least 66% of integers d. Our proofs generally have two steps: bound the average rank of the Jacobian u sing a 3-descent\, and then apply Chabauty-like methods to bound the numbe r of rational points when the rank is small.\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Razan Taha (Purdue University) DTSTART:20210303T190000Z DTEND:20210303T200000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/11 DESCRIPTION:Title: p-adic Measures for Reciprocals of L-functions of Totally Real F ields\nby Razan Taha (Purdue University) as part of University of Oreg on Number Theory Seminar\n\n\nAbstract\nIn 2014\, Gelbart\, Miller\, Panch ishkin\, and Shahidi introduced an analog to part of the Langlands-Shahidi method by constructing certain p-adic L-functions using the non-constant Fourier coefficients of Eisenstein series. In this talk\, we extend their work to totally real number fields. We construct p-adic measures which int erpolate the special values of p-adic L-functions of a totally real field K at negative integers. These measures are defined by analyzing the non-co nstant terms of partial Eisenstein series of the Hilbert modular group.\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Mundy (Columbia University) DTSTART:20210510T220000Z DTEND:20210510T230000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/12 DESCRIPTION:Title: The Skinner--Urban method and the symmetric cube Bloch--Kato con jecture\nby Sam Mundy (Columbia University) as part of University of O regon Number Theory Seminar\n\n\nAbstract\nThe Skinner--Urban method is a general method which can be used to construct nontrivial elements in the B loch--Kato Selmer groups attached to certain Galois representations. After giving a historical overview of the method as well as techniques which pr eceded it\, I will briefly explain how it can be used to construct nontriv ial elements in the Selmer group for the symmetric cube of the Galois repr esentation attached to a level 1 modular form\, under certain standard con jectures. This will take us through the theory of automorphic forms and Ga lois representations for the exceptional group G_2.\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Lassina Dembélé (University of Luxembourg) DTSTART:20210524T210000Z DTEND:20210524T220000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/13 DESCRIPTION:Title: Revisiting the modularity of the abelian surfaces of conductor 2 77\nby Lassina Dembélé (University of Luxembourg) as part of Univers ity of Oregon Number Theory Seminar\n\n\nAbstract\nThere is an isogeny cla ss of semistable abelian surfaces $A$ with good reduction outside $277$ an d $End_Q(A) = \\Z$. The modularity (or paramodularity) of this classe was proved by a team of six people: Armand Brumer\, Ariel Pacetti\, Cris Poor\ , Gonzalo Tornaria\, John Voight and David Yuen. They did so by using the so-called Faltings-Serre method. This was the first known case of the para modularity conjecture. In this work in progress\, I will discuss how to (r e-)prove the modularity of these surfaces by directly applying deformation theory. This could be seen as an explicit approach to deformation theory. \n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Gil Moss (University of Utah) DTSTART:20210426T220000Z DTEND:20210426T230000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/14 DESCRIPTION:Title: Moduli of Langlands parameters\nby Gil Moss (University of U tah) as part of University of Oregon Number Theory Seminar\n\n\nAbstract\n The local Langlands correspondence connects representation of p-adic group s to Langlands parameters\, which are certain representations of Galois gr oups of local fields. In recent work with Dat\, Helm\, and Kurinczuk\, we have shown that Langlands parameters\, when viewed through the right lens\ , occur naturally within a moduli space over Z[1/p]\, and we can say some things about the geometry of this moduli space. This geometry should be re flected in the representation theory of p-adic groups\, on the other side of the local Langlands correspondence. The "local Langlands in families" c onjecture describes the moduli space of Langlands parameters in terms of t he center of the category of representations of the p-adic group-- it was established for GL(n) in 2018. The goal of the talk is to give an overview of this picture\, including current work in-progress\, with some discussi on of the relation with recent work of Zhu and Fargues-Scholze.\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Brandon Williams (RWTH Aachen) DTSTART:20210503T203000Z DTEND:20210503T213000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/15 DESCRIPTION:Title: Borcherds products and a ring of Hermitian modular forms\nby Brandon Williams (RWTH Aachen) as part of University of Oregon Number The ory Seminar\n\n\nAbstract\nWe will compute the ring of modular forms for t he group U(2\, 2) over the integers in Q(\\sqrt{-7}). The main tool is Bor cherds products and their application to Hermitian modular forms due to De rn.\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/15/ END:VEVENT BEGIN:VEVENT SUMMARY:David Lowry-Duda (ICERM) DTSTART:20210517T220000Z DTEND:20210517T230000Z DTSTAMP:20260422T230718Z UID:UOregonNTSeminar/16 DESCRIPTION:Title: Visualizing modular forms\nby David Lowry-Duda (ICERM) as pa rt of University of Oregon Number Theory Seminar\n\n\nAbstract\nWe investi gate ways to visualize modular forms. A good visualization of\na modular f orm should reveal some of the highly symmetric structure of\nthe modular f orm. But different methods of visualization shine different\nspotlights on the modular form. In this talk\, we examine different\nmethods of making and studying these visualizations. Further\, we'll\nexamine both classical and non-classical modular forms in a variety of\ndifferent visualizations . There will be lots and lots of pictures!\n LOCATION:https://researchseminars.org/talk/UOregonNTSeminar/16/ END:VEVENT END:VCALENDAR