{"id":195,"date":"2023-06-14T13:20:12","date_gmt":"2023-06-14T20:20:12","guid":{"rendered":"https:\/\/live-usc-dornsife.pantheonsite.io\/negron\/?page_id=195"},"modified":"2023-06-26T23:44:09","modified_gmt":"2023-06-27T06:44:09","slug":"previous-seminars","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/negron\/previous-seminars\/","title":{"rendered":"Previous Seminars"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
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Topics: Algebra and representation theory, algebraic geometry and topology, mathematical physics<\/span><\/p>\n

Spring 2023<\/p>\n

 <\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Date<\/th>\nRoom<\/th>\nSpeaker<\/th>\nTitle & Abstract<\/th>\n<\/tr>\n
Feb 6<\/td>\nKap 245<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
Feb 13<\/td>\n<\/td>\nBurt Totaro (UCLA)<\/td>\nCalabi-Yau varieties of large index<\/strong><\/p>\n

Abstract: A projective variety is called Calabi-Yau if its canonical divisor is Q-linearly equivalent to zero. The smallest positive integer m with mK_X linearly equivalent to zero is called the index of X. Using ideas from mirror symmetry, we construct Calabi-Yau varieties with index growing doubly exponentially with dimension. We conjecture that our examples have the largest possible index in each dimension. Joint work with Louis Esser and Chengxi Wang.<\/td>\n<\/tr>\n

Feb 20<\/td>\n<\/td>\nHoliday (Wed Feb 22 is possible)<\/td>\n<\/td>\n<\/tr>\n
Feb 27<\/td>\n<\/td>\nAnna Szumowicz (CalTech)<\/td>\nUniform bounds on the Harish-Chandra characters<\/strong><\/p>\n

Abstract: Let G be a connected reductive algebraic group over a p-adic local field F. We study the asymptotic behaviour of the trace characters\u00a0\u03b8_\u03c0\u00a0evaluated at a regular element of G(F) as\u00a0\u03c0\u00a0varies among supercuspidal representations of G(F). Kim, Shin and Templier conjectured that\u00a0\u03b8_\u03c0(\u03b3)\/deg(\u03c0) tends to 0 when\u00a0\u03c0\u00a0runs over irreducible supercuspidal representations of G(F) and the formal degree of\u00a0\u03c0\u00a0tends to infinity. In fact something stronger holds under some additional conditions. I give the sketch of the proof that for G semisimple the trace character is uniformly bounded on\u00a0\u03b3\u00a0under the assumption, which is believed to hold in general, that all irreducible supercuspidal representations of G(F) are compactly induced from an open compact modulo center subgroup.<\/td>\n<\/tr>\n

Mar 6<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
Mar 13<\/td>\n<\/td>\nSpring break<\/td>\n<\/td>\n<\/tr>\n
Mar 20<\/td>\n<\/td>\nWenjun Niu (UC Davis)<\/td>\nQuantum supergroups associated to 3d N=4 abelian gauge theories<\/strong><\/p>\n

Abstract: Vertex algebras have been an important ingredients in the study of braided tensor category of line defects in 3d topological field theories. However, they are not the most convenient to work with, since the theory of intertwining operators is very complicated. In many cases, one has what is called a Kazhdan-Lusztig correspondence, which is an equivalence between braided tensor category of vertex algebra representations and quasi-triangular Hopf algebra representations, and the latter is significantly easier to work with. In this talk, I will introduce quantum supergroups associated to B twists of 3d N=4 abelian gauge theories, whose representation category is equivalent to the category of representations of the boundary vertex algebra as an abelian category. I will explain how the quantum supergroup representation category is braided and how we can upgrade the above equivalence into one of braided tensor categories. This is joint work in progress with T. Creutzig and T. Dimofte.<\/td>\n<\/tr>\n

Mar 27<\/td>\n<\/td>\nCarl Mautner (UC Riverside)<\/td>\nSymmetric groups, Schur algebras and symmetric products of the plane<\/strong><\/p>\n

Abstract:\u00a0In joint work with Tom Braden we introduce a new algebra, a close cousin to the Schur algebra. \u00a0Like the Schur algebra, it can be defined in terms of the symmetric group and has a nice diagrammatic description. \u00a0Geometrically, this algebra appears in our study of perverse sheaves on S^n(C<\/strong>^2), the n-fold symmetric product of the plane. \u00a0In this talk I will aim to describe our motivation for this work and some interesting properties of the algebra.<\/td>\n<\/tr>\n

Apr 3<\/td>\n<\/td>\n[the date is open, but the seminar organizer will be away]<\/td>\n<\/td>\n<\/tr>\n
Apr 10<\/td>\n<\/td>\nHans Wenzl (UCSD)<\/td>\nModule categories of certain fusion categories<\/strong><\/p>\n

Abstract: Module categories can be viewed as the analogue of subgroups for tensor categories. Indeed, all module categories of the category of representations of a finite group can be described in terms of its subgroups.\u00a0 We study module categories of fusion categories coming from quantum groups at roots of unity. These can be classified via so-called modular invariants. We expect that for non-exceptional modular invariants, all of these module categories can be constructed via deformations of certain subgroups of the corresponding Lie group.\u00a0 We present large classes of examples for which this has been checked.<\/td>\n<\/tr>\n

Apr 14, All Day, HNB 100<\/td>\n<\/td>\nMany People<\/td>\nSymposium on noncommutative alg, in honor of Prof. Montgomery<\/strong><\/p>\n

Abstract:\u00a0https:\/\/wise.usc.edu\/event\/symposium-on-noncommutative-algebras-in-honor-of-professor-susan-montgomery\/<\/a><\/p>\n

 <\/td>\n<\/tr>\n

Apr 17<\/td>\n<\/td>\nMatthias Flach (CalTech)<\/td>\nSpecial values of Zeta functions and Deligne cohomology<\/strong><\/p>\n

Abstract:\u00a0We will briefly explain the role played by Deligne cohomology, and more generally certain complexes of locally compact abelian groups, in the conjectural description of special values of Zeta functions of arithmetic schemes as in recent joint work of Morin and myself. We will then, as the main focus of the talk, explain the construction of a category of \u201ccomplete condensed complexes\u201d which combines the liquid and solid condensed complexes of Clausen and Scholze. We argue that this category is the natural home for the type of homological algebra with locally compact abelian groups involved in the description of Zeta values.<\/td>\n<\/tr>\n

Apr 24<\/td>\n<\/td>\nCraig Westerland (UMN)<\/td>\nCohomology of Hurwitz spaces<\/strong><\/p>\n

Abstract:\u00a0\u00a0Hurwitz moduli spaces parameterize branched covers of algebraic curves.\u00a0 In this talk, I\u2019ll focus on branched covers of the affine line and explain several approaches to understanding the cohomology of these moduli spaces using connections to braided Hopf algebras and a new family of braided operads.\u00a0 In particular, I hope to convey how an operad which governs multiplicative operations on Hurwitz spaces also controls primitives in braided Hopf algebras.\u00a0 Time permitting, I\u2019ll also discuss what little can be said about the action of the absolute Galois group on these cohomology rings.<\/td>\n<\/tr>\n

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Previous Semester (S22)<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Date<\/th>\nRoom<\/th>\nSpeaker<\/th>\nTitle & Abstract<\/th>\n<\/tr>\n
\u00a0Feb 7<\/span><\/td>\n\u00a0Kap414<\/span><\/td>\n\u00a0Speaker<\/span><\/td>\nTitle<\/span><\/p>\n

Abstract:<\/td>\n<\/tr>\n

\u00a0Feb 14<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n<\/td>\n<\/tr>\n
\u00a0Feb 21<\/span><\/td>\n<\/td>\nHoliday<\/span><\/td>\n\u00a0<\/span><\/td>\n<\/tr>\n
\u00a0Feb 28<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n<\/tr>\n
\u00a0Mar 7<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n<\/tr>\n
\u00a0Mar 21<\/span><\/td>\n\u00a0<\/span><\/td>\nPaul Balmer (UCLA)
\n<\/span><\/td>\n		The tensor-triangular geometry of permutation modules
\n<\/span>Abstract: Given a finite group G and a field k of positive characteristic p, dividing the order of G, it is well-known that there is in general a wild world of finitely generated kG-modules. This is the complexity of so-called modular representation theory. On the other hand, permutation modules are the k-linearizations of finite G-sets, like the module k(G\/H) for H a subgroup of G. And there are much fewer of the latter. Permutation modules also play a role in a variety of related settings, like for Mackey functors, or for Artin motives. We shall discuss the tt-geometry of the category of bounded complexes of permutations modules, at least in simple examples. This is joint work with Martin Gallauer (Bonn).<\/td>\n<\/tr>\n
\u00a0Mar 28<\/span><\/td>\n\u00a0<\/span><\/td>\nYuri Bakhturin (Memorial Univ)
\n<\/span><\/td>\n		Group Gradings and Actions of Pointed Hopf Algebras
\n<\/span>Abstract: Pointed Hopf algebras are a wide class of Hopf algebras, including group algebras and enveloping algebras of Lie algebras. In this talk, based on a recent work with Susan Montgomery, we study actions of pointed Hopf algebras on simple algebras. These actions are known to be inner, as in the case of Skolem – Noether theorem. We try to give explicit descriptions, whenever possible, and consider Taft algebras, their Drinfeld doubles and some quantum groups.<\/td>\n<\/tr>\n
\u00a0Apr 4<\/span><\/td>\n\u00a0<\/span><\/td>\nSami Assaf (USC)<\/span><\/td>\nA Littlewood-Richardson Rule for Demazure modules<\/span><\/p>\n

Abstract: Demazure modules are submodules of irreducible modules of Lie algebras generated by extremal weight spaces under the action of a Borel subalgebra. For the general linear group, their characters form a basis of polynomials that containing Schur polynomials, the characters of irreducible modules. The celebrated Littlewood-Richardson rule gives a beautiful combinational model for tensoring irreducible modules or, equivalently, multiplying Schur polynomials. The analogous problem for Demazure modules is to give an excellent filtration, but this exists only in certain cases. One sees this computationally since the product of Demazure characters cannot, in general, be written as a nonnegative sum of Demazure characters. In this talk, I\u2019ll present a nonnegative Littlewood-Richardson rule expanding the product of a Demazure character and Schur polynomial into Schubert characters, certain polynomials indexed by lower order ideals in Bruhat order. This combinatorial statement suggests that the tensor product of Demazure modules admits a Schubert filtration, a still open conjecture of Polo from 1989.<\/p>\n

No familiarity with Demazure modules or characters is assumed for this talk.<\/td>\n<\/tr>\n

\u00a0Apr 11<\/span><\/td>\n\u00a0<\/span><\/td>\nBrian Lawrence (UCLA)<\/span><\/td>\nSparsity of Integral Points on Moduli Spaces of Varieties<\/span><\/p>\n

Abstract: Interesting moduli spaces don’t have many integral points. More precisely, if X is a variety over a number field, admitting a variation of Hodge structure whose associate period map is injective, then the number of S-integral points on X of height at most H grows more slowly than H\u03b5<\/sup>, for any positive \u03b5. This is a sort of weak generalization of the Shafarevich conjecture; it is a consequence of a point-counting theorem of Broberg, and the largeness of the fundamental group of X. Joint with Ellenberg and Venkatesh (arxiv:2109.01043<\/a>).<\/td>\n<\/tr>\n

\u00a0Fri Apr 15 @ 2PM!<\/span><\/p>\n

[Special time and day]<\/span><\/td>\n

KAP414\u00a0<\/span><\/td>\nKyle Ormsby (Reed College)<\/span><\/td>\nHochschild homology: classical, topological, and motivic<\/span><\/p>\n

Abstract:\u00a0After giving a historical overview of classical and topological Hochschild homology, I will introduce a motivic variant valued in the stable\u00a0A<\/strong>1<\/sup>-homotopy category. Over the field of complex numbers, computations reveal that motivic Hochschild homology of\u00a0F<\/strong>p<\/sub>\u00a0exhibits a rich pattern of “\u03c4-torsion” elements. I will describe these computations and their significance, concluding with a no-go theorem regarding three potential motivic analogues of classical theorems. The talk will be accessible to those without prior experience in\u00a0A<\/strong>1<\/sup>-homotopy theory. This is joint work with Bjorn Dundas, Mike Hill, and Paul Arne Ostvaer.<\/td>\n<\/tr>\n

\u00a0Apr 18<\/span><\/td>\n\u00a0<\/span><\/td>\nAbhishek Oswal (CalTech)<\/span><\/td>\nAlgebraization theorems in non-archimedean geometry
\n<\/span>Abstract:\u00a0Algebraization theorems originating from o-minimality have found striking applications in recent years to Hodge theory and Diophantine geometry. The utility of o-minimality originates from the ‘tame’ topological properties that sets definable in such structures satisfy. O-minimal geometry thus provides a way to interpolate between the algebraic and analytic worlds. One such algebraization theorem that has been particularly useful is the definable Chow theorem of Peterzil and Starchenko which states that a closed analytic subset of a complex algebraic variety that is simultaneously definable in an o-minimal structure is an algebraic subset. In this talk, I shall discuss a non-archimedean version of this result and time-permitting some recent applications of these algebraization theorems.<\/td>\n<\/tr>\n
\u00a0Apr 25<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0Sam Gunningham (U Montana)<\/span><\/td>\nLanglands duality for 3-manifolds<\/span>
\nAbstract:\u00a0Skein modules are linear spaces spanned by knots and links in a given 3-manifold, modulo certain skein relations. They were defined about 30 years ago independently by Przytycki and Turaev and have been extensively studied in the subsequent years. In this talk I will propose a new role for skein modules: as (a component of) the state space of a certain 4-dimensional topological quantum field theory, which according to the work of Kapustin and Witten, encodes the mathematical features of the geometric Langlands program. This realization leads to some surprising conjectures (which can be directly verified in some key cases), relating two different flavors of skein modules on a given closed 3-manifold. This is joint work with David Ben-Zvi, David Jordan, and Pavel Safronov.<\/td>\n<\/tr>\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n<\/tr>\n
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Previous Semester (F21)<\/span><\/p>\n

\u00a0<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Date<\/th>\nRoom<\/th>\nSpeaker<\/th>\nTitle & Abstract<\/th>\n<\/tr>\n
\u00a0Sep 6<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0Holiday<\/span><\/td>\n\u00a0<\/span><\/td>\n<\/tr>\n
\u00a0Sep 13<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n<\/tr>\n
\u00a0Sep 20<\/span><\/td>\nKap414\u00a0<\/span><\/td>\n\u00a0Elden Elmato (Harvard)<\/span><\/td>\nBott-inverted Grothendieck-Witt theory<\/span><\/p>\n

Abstract:\u00a0Thomason proved that Bott-inverted (or, better, KU-local) algebraic K-theory satisfies \u00e9tale descent. This was decisive in clarifying the Quillen-Lichtenbaum conjectures in algebraic K-theory. It turns out that KU-local Grothendieck-Witt theory is not an etale sheaf in general but instead satisfies Scheiderer’s b-descent. I will explain this result and its connections with Real algebraic geometry. This is joint work with Nardin, Shah and Yang.<\/td>\n<\/tr>\n

\u00a0Sep 27<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0Joshua Swanson (USC)<\/span><\/td>\nDifferential Coinvariant Algebras<\/span><\/p>\n

Abstract:\u00a0The classical coinvariant algebra of a reflection group is a quotient of a polynomial ring by the ideal generated by non-trivial invariants. Coinvariant algebras have their roots in Hilbert’s Basis Theorem and are\u00a0well-understood from a variety of perspectives using tools such as Schubert calculus, symmetric function theory, and monomial bases. A recent conjecture of Zabrocki introduced differential or “super” coinvariant algebras by adding an additional set of *anti*-commuting variables,\u00a0or equivalently by considering coinvariant differential forms. We will describe some of the rich combinatorial and algebraic structure of these differential coinvariant algebras, focusing on the Type A case. Topics include their bi-graded Hilbert series, their alternants, and the homology of certain generalized exterior derivative complexes. Joint work with Nolan Wallach.<\/td>\n<\/tr>\n

\u00a0Oct 4<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0[CAMS career advice panel<\/a>]<\/span><\/td>\n\u00a0<\/span><\/td>\n<\/tr>\n
\u00a0Oct 11<\/span><\/td>\n\u00a0Kap414<\/span><\/td>\n\u00a0Sunghyuk Park (CalTech)<\/span><\/td>\nInverted state sums for knot complements<\/span><\/p>\n

Abstract:\u00a0A couple of years ago, S. Gukov and C. Manolescu conjectured that the Melvin-Morton-Rozansky expansion of the colored Jones polynomials can be resummed into a two-variable series F_K(x,q), as part of a bigger program to construct a 3d TQFT \\hat{Z} that had been predicted from physics.
\nIn this talk, I will explain how to prove their conjecture for a big class of links by “inverting” a state sum.<\/td>\n<\/tr>\n

\u00a0Oct 18<\/span><\/td>\n\u00a0Kap414<\/span><\/td>\n\u00a0Morgan Opie (UCLA)<\/span><\/td>\nChromatic invariants of vector bundles on projective spaces<\/span><\/p>\n

Abstract:\u00a0In this talk, I will outline my work on complex rank 3 topological vector bundles on CP^5. I will describe a classification of such bundles using twisted, topological modular form-valued invariants. This builds a parallel with Atiyah and Rees’ classification of rank 2 topological vector bundles on CP^3, using real k-theory. I will also discuss methods for producing topological vector bundles of rank 3 on CP^5. As time allows, I will outline future directions, including: possible connections between higher real K-theories and vector bundles on projective spaces, and algebraic generalizations of my current work.<\/td>\n<\/tr>\n

\u00a0Oct 25<\/span><\/td>\n\u00a0Kap414<\/span><\/td>\n\u00a0Sergei Gukov (CalTech)<\/span><\/td>\nNon-semisimple TQFTs and BPS q-series<\/span>Abstract:\u00a0We propose and in some cases prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic\u00a0q<\/span><\/span><\/span><\/span>. Both types of invariants are labeled by extra data which plays an important role in the proposed relation. Bridging the two sides — which until recently were developed independently, using very different methods — opens many new avenues. In one direction, it allows to study (and perhaps even to formulate)\u00a0q<\/span><\/span><\/span><\/span>-series invariants labeled by spin<\/span>c<\/span><\/span><\/span><\/span><\/span>\u00a0structures in terms of non-semisimple invariants. In the opposite direction, it offers new insights and perspectives on various elements of non-semisimple TQFT’s, bringing the latter into one unifying framework with other invariants of knots and 3-manifolds that recently found realization in quantum field theory and in string theory.<\/td>\n<\/tr>\n
\u00a0Nov 1<\/span><\/td>\n\u00a0Kap414<\/span><\/td>\n\u00a0Anne Dranowski (USC)<\/span><\/td>\nQuiver Grassmannians and heaps<\/span>Abstract:\u00a0Components of Springer fibers are related to Young tableaux. We recall this relation and describe a generalization using heaps in place of tableaux and a space of modules for the preprojective algebra in place of the flag variety.<\/td>\n<\/tr>\n
\u00a0Nov 8<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n<\/tr>\n
\u00a0Nov 15<\/span><\/td>\n\u00a0Kap414<\/span><\/td>\n\u00a0Rapha\u00ebl Rouquier (UCLA)<\/span><\/td>\nRepresentation theory on spaces<\/span>Abstract:\u00a0I will discuss an emerging theory where geometrical objects arising in representation theory or enumerative geometry are themselves viewed as “representations of a higher group”. More general “higher groups” should arise as invariants of algebraic varieties or categories and I will speculate on connections with K-theory and spaces of stability conditions. I will describe some aspects of the representation theory of the “higher group\u201d associated to a point.<\/td>\n<\/tr>\n
\u00a0Nov 22<\/span><\/td>\n\u00a0Kap414<\/span><\/td>\n\u00a0Masoud Zargar (USC)<\/span><\/td>\nOn spectral gaps<\/span>Abstract:\u00a0Spectral gaps for graphs and the spectral geometry of Riemannian manifolds contain interesting information about the geometry of the underlying objects. Spectral gaps have been studied using various approaches by several people, combining ideas from representation theory, probability theory, and analysis among others. I will explain some of these approaches and state a new result on the spectral gaps of random flat unitary bundles over hyperbolic surfaces.<\/td>\n<\/tr>\n
\u00a0Nov 29<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0Ocupado.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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See our friends at the\u00a0Geometry seminar<\/a>\u00a0(M 2:00 pm) and the\u00a0Combinatorics seminar<\/a>\u00a0(W 2:00 pm).<\/p>\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":279,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-195","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nPrevious Seminars - Cris Negron<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dornsife.usc.edu\/negron\/previous-seminars\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Previous Seminars - Cris Negron\" \/>\n<meta property=\"og:url\" content=\"https:\/\/dornsife.usc.edu\/negron\/previous-seminars\/\" \/>\n<meta property=\"og:site_name\" content=\"Cris Negron\" \/>\n<meta property=\"article:modified_time\" content=\"2023-06-27T06:44:09+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/dornsife.usc.edu\/negron\/previous-seminars\/\",\"url\":\"https:\/\/dornsife.usc.edu\/negron\/previous-seminars\/\",\"name\":\"Previous Seminars - 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