BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ananth Shankar (MIT) DTSTART:20200506T150000Z DTEND:20200506T160000Z DTSTAMP:20260513T182027Z UID:CMI/1 DESCRIPTION:Title: A fi niteness criterion for 2-dimensional representations of surface groups.\nby Ananth Shankar (MIT) as part of CMI seminar series\n\n\nAbstract\nLe t C be a a complex algebraic curve of genus \\geq 1\, and let pi be its fu ndamental group. Let \\rho: pi\\rightarrow \\GL_2(\\C) be a semisimple 2-d imensional representation\, such that \\rho(\\alpha) has finite order for every simple closed loop \\alpha. We will prove that \\rho has finite imag e. If time permits\, we will mention applications of this result to the Gr othendieck-Katz p-curvature conjecture. This is joint work with Anand Pate l and Junho Peter Whang.\n LOCATION:https://researchseminars.org/talk/CMI/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Chandrasekhar Raju (École Polytechnique Fédérale Laussane) DTSTART:20200508T123000Z DTEND:20200508T133000Z DTSTAMP:20260513T182027Z UID:CMI/2 DESCRIPTION:Title: Conn ections between the circle method\, trace formula and bounds for the subco nvexity problem.\nby Chandrasekhar Raju (École Polytechnique Fédéra le Laussane) as part of CMI seminar series\n\n\nAbstract\nAfter introducin g the sub-convexity problem for L-functions in a general context\, we will focus our attention to the particular case of Rankin-Selberg L-functions. We will briefly trace the history of this particular problem starting fro m Kowalski\, Michel\, and Vanderkam\, with a lot of authors in between upt o the seminal work of Michel\, Venkatesh. I will then try to explain how t he circle method enters this question by sketching an argument of Munshi f or what is perhaps the simplest case i.e character twists of GL(2) L-funct ions. I will end the talk by explaining how we can solve the Subconvexity problem for Rankin-Selberg L-functions in the combined level aspect by a v ery easy version of the circle method and see how this approach is connect ed to earlier work on the same problem.\n LOCATION:https://researchseminars.org/talk/CMI/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Akash Sengupta (Columbia University) DTSTART:20200511T150000Z DTEND:20200511T160000Z DTSTAMP:20260513T182027Z UID:CMI/3 DESCRIPTION:Title: Geom etric invariants and geometric consistency of Manin's conjecture.\nby Akash Sengupta (Columbia University) as part of CMI seminar series\n\n\nAb stract\nLet X be a Fano variety with an associated height function defined over a number field. Manin's conjecture predicts that\, after removing a thin set\, the growth of the number of rational points of bounded height o n X is controlled by certain geometric invariants (e.g. the Fujita invaria nt of X). I will talk about how to use birational geometric methods to stu dy the behaviour of these invariants and propose a geometric description o f the thin set in Manin's conjecture. Part of this is joint work with Bria n Lehmann and Sho Tanimoto.\n LOCATION:https://researchseminars.org/talk/CMI/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Mohan Swaminathan (Princeton University) DTSTART:20200513T150000Z DTEND:20200513T160000Z DTSTAMP:20260513T182027Z UID:CMI/4 DESCRIPTION:Title: A co ncrete approach to virtual classes in genus 0 Gromov--Witten theory\nb y Mohan Swaminathan (Princeton University) as part of CMI seminar series\n \n\nAbstract\nGromov--Witten theory is concerned with counting curves insi de (smooth) projective varieties satisfying some incidence conditions (e.g . how many rational degree d curves pass through 3d-1 generic points in th e complex projective plane?). In general (due to complications arising fro m the fact that spaces of curves may not be smooth)\, instead of counting curves directly\, we need to use intersection theory on the space of curve s to define certain "virtual counts". In the first half of the talk\, we w ill provide the necessary background (spaces of curves\, "expected dimensi on"\, compactness and some examples of curve counting). In the second half of the talk\, we will describe a concrete differential geometric approach to these "virtual counts" for genus 0 curves in projective varieties (usi ng ideas coming from the theory of psuedo-holomorphic curves in symplectic manifolds).\n LOCATION:https://researchseminars.org/talk/CMI/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Akashdeep Dey (Princeton University) DTSTART:20200518T150000Z DTEND:20200518T160000Z DTSTAMP:20260513T182027Z UID:CMI/5 DESCRIPTION:Title: A co mparison of the Almgren-Pitts and the Allen-Cahn min-max theory.\nby A kashdeep Dey (Princeton University) as part of CMI seminar series\n\n\nAbs tract\nMin-max theory for the area functional was developed by Almgren and Pitts to construct closed minimal hypersurfaces in an arbitrary closed Ri emannian manifold. There is an alternate approach via PDE to the construct ion of minimal hypersurfaces. This approach is based on the study of the l imiting behaviour of solutions to the Allen-Cahn equation. In my talk\, I will briefly describe the Amgren-Pitts min-max theory and the Allen-Cahn m in-max theory and discuss the question to what extent these two theories a gree.\n LOCATION:https://researchseminars.org/talk/CMI/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Alapan Mukhopadhyay (University of Michigan\, Ann Arbor) DTSTART:20200520T150000Z DTEND:20200520T160000Z DTSTAMP:20260513T182027Z UID:CMI/6 DESCRIPTION:Title: Sing ularities in positive characteristics.\nby Alapan Mukhopadhyay (Univer sity of Michigan\, Ann Arbor) as part of CMI seminar series\n\n\nAbstract\ nIn the first half\, we shall look at the several notions of singularities of a polynomial function at a point from both analytic and algebro-geomte ric point of view. We will indicate the surprising similarities of the res ults coming from these two seemingly different directions. In the second h alf\, these ideas will be put into a more general context detailing more o n the positive characteristic side. We shall discuss the notion of F-split \, F-regular schemes\, how these notions are related to the characteristic zero singularities. We shall end by mentioning some open problems relatin g singularities in characteristic zero and positive characteristic. This t alk is an exposition of the ideas developed in the last fifty years in dif ferent contexts.\n LOCATION:https://researchseminars.org/talk/CMI/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Arnab Saha (Indian Institute of Technology (IIT) Gandhinagar) DTSTART:20200525T123000Z DTEND:20200525T133000Z DTSTAMP:20260513T182027Z UID:CMI/7 DESCRIPTION:Title: $p$- adic Hodge theory and delta geometry\nby Arnab Saha (Indian Institute of Technology (IIT) Gandhinagar) as part of CMI seminar series\n\n\nAbstra ct\nWe will talk about a new $p$-adic Galois representation that comes fro m $\\delta$-geometry. Here\, we construct a new filtered Isocrystal associ ated to an abelian scheme that is different from the usual crystalline coh omology. In the case of elliptic curves\, depending on a modular parameter \, this Isocrystal is also weakly admissible which leads to a new crystall ine Galois representation attached to the elliptic curve via the Fontaine functor. This is joint work with Jim Borger. \n\nWe will dedicate the firs t half of the talk on giving an overview of $p$-adic Hodge theory and $\\d elta$-geometry.\n LOCATION:https://researchseminars.org/talk/CMI/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Utsav Choudhury (Indian Statistical Institute (ISI)\, Kolkata) DTSTART:20200710T123000Z DTEND:20200710T140000Z DTSTAMP:20260513T182027Z UID:CMI/8 DESCRIPTION:Title: Unst able motivic homotopy theory and few commutative algebra problems\nby Utsav Choudhury (Indian Statistical Institute (ISI)\, Kolkata) as part of CMI seminar series\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/CMI/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Siddhi Pathak (Pennsylvania State University) DTSTART:20200529T123000Z DTEND:20200529T133000Z DTSTAMP:20260513T182027Z UID:CMI/9 DESCRIPTION:Title: Arit hmetic nature of special values of L-functions\nby Siddhi Pathak (Penn sylvania State University) as part of CMI seminar series\n\n\nAbstract\nTh e study of L-functions has occupied a center stage in number theory since the work of Riemann and Dirichlet. A standard example of an L-function is the Riemann zeta-function\, $\\zeta(s)$\, given by the series $\\sum_{n=1 }^{\\infty} n^{-s}$ when $\\Re(s)>1$. The aim of this talk will be to disc uss the question of determining the arithmetic nature (that is\, rational/ irrational and algebraic/transcendental) of values of L-functions at posit ive integers. For example\, it is expected that the values $\\zeta(m)$ are transcendental for all integers $m >1$. However\, the only known cases of this conjecture are the even zeta-values\, which Euler had explicitly eva luated in the 1730s. Among the odd zeta-values\, Apery proved that $\\zeta (3)$ is irrational\, whereas the irrationality of the remaining odd zeta-v alues remains a mystery. \n\nIn this talk\, we will discuss various facets of this problem. If time permits\, we will prove that for a fixed odd pos itive integer m\, all the values $\\zeta_K(m)$ are irrational as K varies over imaginary quadratic fields\, with at most one possible exception. Thi s is joint work with Ram Murty. This talk will be accessible to a wide aud ience.\n LOCATION:https://researchseminars.org/talk/CMI/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Ronno Das (University of Chicago) DTSTART:20200708T123000Z DTEND:20200708T133000Z DTSTAMP:20260513T182027Z UID:CMI/10 DESCRIPTION:Title: Non collinear points in the projective plane\nby Ronno Das (University of Chicago) as part of CMI seminar series\n\n\nAbstract\nWe will look at the space of n points in the projective plane such that no three lie on the sa me line. There is an action of the symmetric group by permuting the points and we can compute the action on cohomology (for n < 7) by counting the n umbers of such n tuples over the finite field F_q\, with a 'twist'. Unfort unately for n > 6 such a computation is still hard and we expect the answe r for large n to be arbitrarily complicated (in the sense of Mnëv's unive rsality). This talk will be based on joint work with Ben O'Connor.\n LOCATION:https://researchseminars.org/talk/CMI/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Arul Shankar (University of Toronto) DTSTART:20200603T150000Z DTEND:20200603T160000Z DTSTAMP:20260513T182027Z UID:CMI/11 DESCRIPTION:Title: Squ arefree sieves in arithmetic statistics\nby Arul Shankar (University o f Toronto) as part of CMI seminar series\n\n\nAbstract\nA classical questi on in analytic number theory is: given a polynomial with integer coefficie nts\, how often does it take squarefree values? In arithmetic statistics\, we are particularly interested in the case of discriminant polynomials. I n this talk\, I will present several different cases of this question. Fir st\, we will consider a classical result of Davenport--Heilbronn which con siders the case of discriminants of binary cubic forms. Then\, I will disc uss joint work with Bhargava in which we consider the case of discriminant s of ternary cubic forms.\n\nThird\, I will describe joint and ongoing wor k with Bhargava and Wang\, in which we consider different families of degr ee-n polynomials in one variable\, and determine the proportion of those h aving squarefree discriminant. Finally\, I will describe various applicati ons of these results\n LOCATION:https://researchseminars.org/talk/CMI/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Abhishek Oswal (University of Toronto) DTSTART:20200608T150000Z DTEND:20200608T160000Z DTSTAMP:20260513T182027Z UID:CMI/12 DESCRIPTION:Title: A n on-archimedean definable Chow theorem.\nby Abhishek Oswal (University of Toronto) as part of CMI seminar series\n\n\nAbstract\nO-minimality has had some striking applications to number theory.\nThe utility of o-minimal structures originates from the remarkably\ntame topological properties sa tisfied by sets definable in such\nstructures. Despite the rigidity that i t imposes\, the theory is\nsufficiently flexible to allow for a range of a nalytic constructions.\nAn illustration of this `tame' property is the fol lowing surprising\ngeneralization of Chow's theorem proved by Peterzil and Starchenko -\nA closed analytic subset of a complex algebraic variety tha t is also\ndefinable in an o-minimal structure\, is in fact algebraic. Whi le the\no-minimal machinery aims to capture the archimedean order topology of the\nreal line\, it is natural to wonder if such a machinery can be se t up over\nnon-archimedean fields. In this talk\, we explore a non-archime dean\nanalogue of an o-minimal structure and describe a version of the def inable\nChow theorem in this context.\n LOCATION:https://researchseminars.org/talk/CMI/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Baskar Balasubramanyam (Indian Institute of Science Education and Research (IISER)\, Pune) DTSTART:20200611T123000Z DTEND:20200611T133000Z DTSTAMP:20260513T182027Z UID:CMI/13 DESCRIPTION:Title: Con struction of p-adic L-functions\nby Baskar Balasubramanyam (Indian Ins titute of Science Education and Research (IISER)\, Pune) as part of CMI se minar series\n\n\nAbstract\nIn this talk\, I will discuss some of the cons tructions of p-adic L-functions that interpolates families of classical sp ecial values. Finally\, I will talk about the construction of the p-adic a djoint L-functions using overconvergent cohomology. I will try to keep thi s talk accessible to as wide an audience as possible.\n LOCATION:https://researchseminars.org/talk/CMI/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Padmavathi Srinivasan (University of Georgia) DTSTART:20200615T150000Z DTEND:20200615T160000Z DTSTAMP:20260513T182027Z UID:CMI/14 DESCRIPTION:Title: Top ological invariants in arithmetic geometry\nby Padmavathi Srinivasan ( University of Georgia) as part of CMI seminar series\n\n\nAbstract\nThis w ill be a gentle introduction to two independent themes.\n\nThe first half of the talk will focus on conductors and discriminants\, two invariants th at measure degeneration in a family of a hyperelliptic curves. We will sho w how a combinatorial refinement helps us compare these two invariants.\n\ nThe second half of the talk will be be an introduction to A^1 enumerative geometry\, i.e.\, how we may use quadratic forms to encode additional ari thmetic information in enumerative problems in algebraic geometry.\n LOCATION:https://researchseminars.org/talk/CMI/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Ved Datar (Indian Institute of Science (IISc) Bangalore) DTSTART:20200617T123000Z DTEND:20200617T133000Z DTSTAMP:20260513T182027Z UID:CMI/15 DESCRIPTION:Title: (In verse)-Hessian type equations and positivity in complex algebraic geometry \nby Ved Datar (Indian Institute of Science (IISc) Bangalore) as part of CMI seminar series\n\n\nAbstract\nIn the early 2000's Demailly and Paun proved that a (1\,1) cohomology class on a K\\"ahler manifold is positive if and only if certain intersection numbers are positive. This is a gener alization of the classical Nakai criteria for ampleness of line bundles on projective manifolds. The proof\, somewhat surprisingly\, relies on Yau's work on the complex Monge-Ampere equation\, and his solution to the Calab i conjecture. In 2019\, Gao Chen extended the method of Demailly-Paun to p rove that another important PDE in Kahler geometry\, namely the J-equation \, is equivalent to the positivity of certain (twisted) intersection numbe rs\, thereby settling a conjecture of Lejmi and Szekelyhidi. In my talk\, I will describe this circle of ideas\, concluding with a recent result obt ained in collaboration with Vamsi Pingali extending the work of Gao Chen t o more general inverse Hessian type equations\, thereby settling a conject ure of Szekelyhidi for projective manifolds. In the process we obtain an e quivariant version of Gao Chen's result\, and in particular recover some r esults of Collins and Szekelyhidi on the J-equation on toric manifolds.\n LOCATION:https://researchseminars.org/talk/CMI/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Swarnava Mukhopadhyay (Tata Institute of Fundamental Research (TIF R) Mumbai) DTSTART:20200622T123000Z DTEND:20200622T133000Z DTSTAMP:20260513T182027Z UID:CMI/16 DESCRIPTION:Title: Gra ph potentials and Moduli spaces of vector bundles of curves\nby Swarna va Mukhopadhyay (Tata Institute of Fundamental Research (TIFR) Mumbai) as part of CMI seminar series\n\n\nAbstract\nWe construct and study graph pot entials\, a collection of Laurent polynomials associated with colored grap hs of small valency. The potentials we construct are related to the moduli spaces of vector bundles of rank two with fixed determinant on algebraic curves. We will discuss relations between these graph potentials and Gromo v-Witten invariants of the moduli spaces. This is joint work with P. Belma ns and S. Galkin.\n LOCATION:https://researchseminars.org/talk/CMI/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Yajnaseni Dutta (University of Bonn) DTSTART:20200624T123000Z DTEND:20200624T133000Z DTSTAMP:20260513T182027Z UID:CMI/17 DESCRIPTION:Title: Pos itivity of direct image sheaves\nby Yajnaseni Dutta (University of Bon n) as part of CMI seminar series\n\n\nAbstract\nPositivity properties of d irect image sheaves have deep implications in\nthe geometry of families of varieties. For instance\, the existence of\nenough global sections of pus hforwards of higher tensors of the relative\ncanonical bundle of a family\ , puts certain restrictions on the kinds of\nvarieties that can appear on the fibres etc. I will discuss some these\npositivity properties\, especia lly the ones that come as a generalisation\nof the Fujita conjecture and i ts application to the Iitaka conjecture. This is\npartially a joint work w ith Takumi Murayama.\n LOCATION:https://researchseminars.org/talk/CMI/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Nivedita Bhaskar (University of Southern California) DTSTART:20200629T150000Z DTEND:20200629T160000Z DTSTAMP:20260513T182027Z UID:CMI/18 DESCRIPTION:Title: Bra uer p-dimensions of complete discretely valued fields\nby Nivedita Bha skar (University of Southern California) as part of CMI seminar series\n\n \nAbstract\n(This is joint work with Bastian Haase) To every central simpl e algebra A over a field F\, one can associate two numerical Brauer class invariants called the index(A) and the period(A). It is well known from th at index(A) divides high powers of per(A). The Brauer dimension of a field F is defined to be the least number n such that index(A) divides period(A )^n for every central simple algebra A defined over any finite extension o f F. Similarly there exist analogous notions of Brauer-p-dimensions of fie lds. The 'period-index' questions revolve around bounding the Brauer (p) d imensions of arbitrary fields.\n\nIn this talk\, we will look at the perio d-index question over complete discretely valued fields in the so-called ' bad characteristic' case (i.e when the residue field has characteristic p) . We will give a flavour of the known results for this question and discus s progress for the cases when the residue fields have small 'p-ranks'. Fin ally\, we will propose a (still open!) conjecture which very precisely rel ates the Brauer p-dimensions of the complete discretely valued fields to t he p-ranks of the residue fields\, along with some evidence via a family o f examples. The key idea involves working with Kato's filtrations and boun ding the symbol length of the second Milnor K group modulo p in a concrete manner\, which further relies on the machinery of differentials in charac teristic p as developed by Cartier.\n LOCATION:https://researchseminars.org/talk/CMI/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Chiranjib Mukherjee (University of Münster) DTSTART:20200701T123000Z DTEND:20200701T133000Z DTSTAMP:20260513T182027Z UID:CMI/19 DESCRIPTION:Title: The Kardar-Parisi-Zhang equation in $d\\geq 3$ and the Gaussian free field\nby Chiranjib Mukherjee (University of Münster) as part of CMI seminar series\n\n\nAbstract\nThe Kardar-Parisi-Zhang (KPZ) equation is a singular stochastic partial differential equation (SPDE) and belongs to a large cl ass of models known as the KPZ universality class\, which is believed to e xhibit very different behavior than Gaussian universality class and descri be \nthe long-time of a wide class of systems including some noisy SPDEs\, driven lattice gases\, randomly growing interfaces and directed polymers in random media. In spatial dimension one\, recently this class has been s tudied extensively based on approximations by exactly solvable models. wh ich no longer exist if perturbations appear in the approximating models\, or when higher dimensional models are investigated. When the spatial dime nsion is at least three\, it was conjectured that two disjoint universalit y classes co-exist when the long-time/large-scale behavior of the solution s are studied. We will report some recent progress along these directions. \n LOCATION:https://researchseminars.org/talk/CMI/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Agnid Banerjee (TIFR Centre For Applicable Mathematics\, Bangalore ) DTSTART:20200706T123000Z DTEND:20200706T133000Z DTSTAMP:20260513T182027Z UID:CMI/20 DESCRIPTION:Title: The structure of the regular and the singular set of the free boundary in the obstacle problem for fractional heat equation.\nby Agnid Banerjee (TI FR Centre For Applicable Mathematics\, Bangalore) as part of CMI seminar s eries\n\n\nAbstract\nIn this talk\, I will discuss the structure of the fr ee boundary in the obstacle problem for fractional powers of the heat oper ator. Our results are derived from the study of a lower dimensional obstac le problem for a class of local\, but degenerate\, parabolic equations. Th e analysis will be based on new Almgren\, Weiss and Monneau type monotonic ity formulas and the associated blow-up analysis. This is a joint work wit h D. Danielli\, N. Garofalo and A. Petrosyan.\n LOCATION:https://researchseminars.org/talk/CMI/20/ END:VEVENT END:VCALENDAR