BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Owen Gwilliam (UMass) DTSTART:20200930T193000Z DTEND:20200930T203000Z DTSTAMP:20260422T225922Z UID:penncolloquium/1 DESCRIPTION:Title: Spontaneous symmetry breaking\, a view from derived geometry\nb y Owen Gwilliam (UMass) as part of UPenn Mathematics Colloquium\n\n\nAbstr act\nWe will give an overview of how physics and homological algebra have met in the setting of gauge theory\, with an emphasis on how the new subje ct of derived geometry provides a clarifying framework. The talk's concret e aim is to explain the Higgs mechanism as a case study. Our approach will be low-tech and will emphasize the motivations\; anyone familiar with not ions like vector bundle and cochain complex should be able to follow.\n LOCATION:https://researchseminars.org/talk/penncolloquium/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlos Simpson (Nice\, visiting IAS) DTSTART:20201014T193000Z DTEND:20201014T203000Z DTSTAMP:20260422T225922Z UID:penncolloquium/2 DESCRIPTION:Title: Classification of finite algebraic objects\nby Carlos Simpson ( Nice\, visiting IAS) as part of UPenn Mathematics Colloquium\n\n\nAbstract \nI'll report on my current work in progress about the classification of s emigroups and finite categories. This will include a quick introductionto neural networks\, and a discussion of how they can help in the classificat ion proofs. We'll also look at some potential applications to construction problems in algebraic geometry.\n LOCATION:https://researchseminars.org/talk/penncolloquium/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Bamler (UC Berkeley) DTSTART:20201028T193000Z DTEND:20201028T203000Z DTSTAMP:20260422T225922Z UID:penncolloquium/3 DESCRIPTION:Title: Recent developments in Ricci flow\nby Richard Bamler (UC Berkel ey) as part of UPenn Mathematics Colloquium\n\n\nAbstract\nRicci flows are a powerful geometric-analytical tool\, as they have been used to prove im portant results in low-dimensional topology. \n\n \n\nIn the first part of this talk I will focus on Ricci flows in dimension 3. I will briefly revi ew Perelman’s construction of Ricci flow with surgery\, which led to the resolution of the Poincar\\’e and Geometrization Conjectures. Then I wi ll discuss recent work of Lott\, Kleiner and myself on an improved version of this flow\, called “singular Ricci flow”. This work allowed us to resolve the Generalized Smale Conjecture\, concerning the structure of dif feomorphism groups\, and a conjecture concerning the contractibility of th e space of positive scalar curvature metrics on 3-manifolds.\n\n \n\nIn th e second part of the talk\, I will focus on Ricci flows in higher dimensio ns. I will present a new compactness\, which can be used to study the sing ularity formation of the flow\, as well as its long-time asymptotics. I wi ll discuss these and some further consequences. I will also convey some in tuition of the new terminology that had to be introduced in connection wit h this compactness theory.\n LOCATION:https://researchseminars.org/talk/penncolloquium/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Benson Farb (U Chicago) DTSTART:20201202T203000Z DTEND:20201202T213000Z DTSTAMP:20260422T225922Z UID:penncolloquium/4 DESCRIPTION:Title: Hilbert's 13th problem\nby Benson Farb (U Chicago) as part of U Penn Mathematics Colloquium\n\n\nAbstract\nHilbert's 13th Problem (H13) is a fundamental open problem about polynomials in one variable. It is part of a beautiful (but mostly forgotten) story going back 3 thousand years. In this talk I will explain how H13 (and related problems) fits into a wi der framework that includes problems in enumerative algebraic geometry and the theory of modular functions. I will then report on some recent progre ss\, joint with Mark Kisin and Jesse Wolfson. While some fancy objects wi ll appear in this talk\, much of it should (I hope) be understandable to u ndergraduate math majors.\n LOCATION:https://researchseminars.org/talk/penncolloquium/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Aleksandr Logunov (Princeton) DTSTART:20210127T203000Z DTEND:20210127T213000Z DTSTAMP:20260422T225922Z UID:penncolloquium/5 DESCRIPTION:Title: Zero sets of Laplace eigenfunctions\nby Aleksandr Logunov (Prin ceton) as part of UPenn Mathematics Colloquium\n\n\nAbstract\nIn the begin ning of 19th century Napoleon set a prize for the best mathematical explan ation of Chladni’s resonance experiments. Nodal geometry studies the zer oes of solutions to elliptic differential equations such as the visible cu rves that appear in these physical experiments. We will discuss geometrica l and analytic properties of zero sets of harmonic functions and eigenfunc tions of the Laplace operator. For harmonic functions on the plane there i s an interesting relation between local length of the zero set and the gro wth of harmonic functions. The larger the zero set is\, the faster the gro wth of harmonic function should be and vice versa. Zero sets of Laplace ei genfunctions on surfaces are unions of smooth curves with equiangular inte rsections. Topology of the zero set can be quite complicated\, but Yau con jectured that the total length of the zero set is comparable to the square root of the eigenvalue for all eigenfunctions. We will start with open qu estions about spherical harmonics and will explain some methods to study n odal sets.\n LOCATION:https://researchseminars.org/talk/penncolloquium/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Kathryn Hess (École Polytechnique Fédérale de Lausanne) DTSTART:20210210T203000Z DTEND:20210210T213000Z DTSTAMP:20260422T225922Z UID:penncolloquium/6 DESCRIPTION:Title: Trees\, barcodes\, and symmetric groups\nby Kathryn Hess (Écol e Polytechnique Fédérale de Lausanne) as part of UPenn Mathematics Collo quium\n\n\nAbstract\nMotivated by the desire to automate classification of neuron morphologies\, we designed a topological signature\, the Topologic al Morphology Descriptor (TMD)\, that assigns a barcode to any geometric tree (i.e\, any finite binary tree embedded in R^3). We showed that the TM D effectively determines the reliability of clusterings of random and neur onal trees. Moreover\, using the TMD we performed an objective\, stable cl assification of pyramidal cells in the rat neocortex\, based only on the s hape of their dendrites.\nWe have also reverse-engineered the TMD\, in ord er to digitally synthesize dendrites\, to compensate for the dearth of ava ilable biological reconstructions. The algorithm we developed\, called Top ological Neuron Synthesis (TNS)\, stochastically generates a geometric tre e from a barcode\, in a biologically grounded manner. The synthesized cort ical dendrites are statistically indistinguishable from the corresponding reconstructed dendrites in terms of morpho-electrical properties and the n etworks they form. We synthesized cortical networks of structurally altere d dendrites\, revealing principles linking branching properties to the str ucture of large-scale networks.\nIn this talk I will provide an overview o f the TMD and the TNS and then describe the results of our theoretical and computational analysis of their behavior and properties\, in which symmet ric groups play a key role. In particular\, I will specify the extent to which the TNS provides an inverse to the TMD. \nThis is joint work with Ad élie Garin and Lida Kanari\, building on earlier collaborations led by Li da Kanari.\n LOCATION:https://researchseminars.org/talk/penncolloquium/6/ END:VEVENT END:VCALENDAR