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:20260404T111329Z UID:penncolloquium/1 DESCRIPTION:Title: Spontaneous symmetry breaking\, a view from derived geometry \nby Owen Gwilliam (UMass) as part of UPenn Mathematics Colloquium\n\n \nAbstract\nWe will give an overview of how physics and homological algebr a have met in the setting of gauge theory\, with an emphasis on how the ne w subject of derived geometry provides a clarifying framework. The talk's concrete aim is to explain the Higgs mechanism as a case study. Our approa ch will be low-tech and will emphasize the motivations\; anyone familiar w ith notions like vector bundle and cochain complex should be able to follo w.\n LOCATION:https://stable.researchseminars.org/talk/penncolloquium/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlos Simpson (Nice\, visiting IAS) DTSTART:20201014T193000Z DTEND:20201014T203000Z DTSTAMP:20260404T111329Z UID:penncolloquium/2 DESCRIPTION:Title: Classification of finite algebraic objects\nby Carlos Si mpson (Nice\, visiting IAS) as part of UPenn Mathematics Colloquium\n\n\nA bstract\nI'll report on my current work in progress about the classificati on of semigroups and finite categories. This will include a quick introduc tionto neural networks\, and a discussion of how they can help in the clas sification proofs. We'll also look at some potential applications to const ruction problems in algebraic geometry.\n LOCATION:https://stable.researchseminars.org/talk/penncolloquium/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Bamler (UC Berkeley) DTSTART:20201028T193000Z DTEND:20201028T203000Z DTSTAMP:20260404T111329Z UID:penncolloquium/3 DESCRIPTION:Title: Recent developments in Ricci flow\nby Richard Bamler (UC Berkeley) as part of UPenn Mathematics Colloquium\n\n\nAbstract\nRicci fl ows are a powerful geometric-analytical tool\, as they have been used to p rove important 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 brief ly review Perelman’s construction of Ricci flow with surgery\, which led to the resolution of the Poincar\\’e and Geometrization Conjectures. Th en I will 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 diffeomorphism groups\, and a conjecture concerning the contractibilit y of the space of positive scalar curvature metrics on 3-manifolds.\n\n \n \nIn the second part of the talk\, I will focus on Ricci flows in higher d imensions. I will present a new compactness\, which can be used to study t he singularity formation of the flow\, as well as its long-time asymptotic s. I will discuss these and some further consequences. I will also convey some intuition of the new terminology that had to be introduced in connect ion with this compactness theory.\n LOCATION:https://stable.researchseminars.org/talk/penncolloquium/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Benson Farb (U Chicago) DTSTART:20201202T203000Z DTEND:20201202T213000Z DTSTAMP:20260404T111329Z UID:penncolloquium/4 DESCRIPTION:Title: Hilbert's 13th problem\nby Benson Farb (U Chicago) as pa rt of UPenn 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 in to a wider framework that includes problems in enumerative algebraic geome try and the theory of modular functions. I will then report on some recent progress\, joint with Mark Kisin and Jesse Wolfson. While some fancy obj ects will appear in this talk\, much of it should (I hope) be understandab le to undergraduate math majors.\n LOCATION:https://stable.researchseminars.org/talk/penncolloquium/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Aleksandr Logunov (Princeton) DTSTART:20210127T203000Z DTEND:20210127T213000Z DTSTAMP:20260404T111329Z UID:penncolloquium/5 DESCRIPTION:Title: Zero sets of Laplace eigenfunctions\nby Aleksandr Loguno v (Princeton) as part of UPenn Mathematics Colloquium\n\n\nAbstract\nIn th e beginning of 19th century Napoleon set a prize for the best mathematical explanation of Chladni’s resonance experiments. Nodal geometry studies the zeroes of solutions to elliptic differential equations such as the vis ible curves that appear in these physical experiments. We will discuss geo metrical and analytic properties of zero sets of harmonic functions and ei genfunctions of the Laplace operator. For harmonic functions on the plane there is an interesting relation between local length of the zero set and the growth of harmonic functions. The larger the zero set is\, the faster the growth of harmonic function should be and vice versa. Zero sets of Lap lace eigenfunctions on surfaces are unions of smooth curves with equiangul ar intersections. Topology of the zero set can be quite complicated\, but Yau conjectured 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 questions about spherical harmonics and will explain some methods to study nodal sets.\n LOCATION:https://stable.researchseminars.org/talk/penncolloquium/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Kathryn Hess (École Polytechnique Fédérale de Lausanne) DTSTART:20210210T203000Z DTEND:20210210T213000Z DTSTAMP:20260404T111329Z UID:penncolloquium/6 DESCRIPTION:Title: Trees\, barcodes\, and symmetric groups\nby Kathryn Hess (École Polytechnique Fédérale de Lausanne) as part of UPenn Mathematic s Colloquium\n\n\nAbstract\nMotivated by the desire to automate classifica tion of neuron morphologies\, we designed a topological signature\, the To pological Morphology Descriptor (TMD)\, that assigns a barcode to any geo metric tree (i.e\, any finite binary tree embedded in R^3). We showed that the TMD effectively determines the reliability of clusterings of random a nd neuronal trees. Moreover\, using the TMD we performed an objective\, st able classification of pyramidal cells in the rat neocortex\, based only o n the shape of their dendrites.\nWe have also reverse-engineered the TMD\, in order to digitally synthesize dendrites\, to compensate for the dearth of available biological reconstructions. The algorithm we developed\, cal led Topological Neuron Synthesis (TNS)\, stochastically generates a geomet ric tree from a barcode\, in a biologically grounded manner. The synthesiz ed cortical dendrites are statistically indistinguishable from the corresp onding reconstructed dendrites in terms of morpho-electrical properties an d the networks they form. We synthesized cortical networks of structurally altered dendrites\, revealing principles linking branching properties to the structure of large-scale networks.\nIn this talk I will provide an ove rview of the TMD and the TNS and then describe the results of our theoreti cal and computational analysis of their behavior and properties\, in which symmetric groups play a key role. In particular\, I will specify the ext ent to which the TNS provides an inverse to the TMD. \nThis is joint work with Adélie Garin and Lida Kanari\, building on earlier collaborations le d by Lida Kanari.\n LOCATION:https://stable.researchseminars.org/talk/penncolloquium/6/ END:VEVENT END:VCALENDAR