BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alessio Figalli (ETH) DTSTART:20210524T130000Z DTEND:20210524T140000Z DTSTAMP:20260422T212553Z UID:GGLectures/1 DESCRIPTION:Title: Quantitative stability in geometric and functional inequalities\, I \nby Alessio Figalli (ETH) as part of Göran Gustafsson Lectures in Mathem atics\n\n\nAbstract\nGeometric and functional inequalities play a crucial role in several problems arising in analysis and geometry. The issue of th e sharpness of a constant\, as well as the characterization of minimizers\ , is a classical and important question. More recently\, there has been a growing interest in studying the stability of such inequalities. The basic question one wants to address is the following:\n\nSuppose we are given a functional inequality for which minimizers are known. Can we quantitative ly show that if a function “almost attains the equality\,” then it is close to one of the minimizers?\n\nIn this series of lectures\, I will fir st give an overview of this beautiful topic and then discuss some recent r esults concerning the Sobolev\, isoperimetric\, and Brunn–Minkowski ineq ualities.\n LOCATION:https://researchseminars.org/talk/GGLectures/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessio Figalli (ETH) DTSTART:20210525T120000Z DTEND:20210525T130000Z DTSTAMP:20260422T212553Z UID:GGLectures/2 DESCRIPTION:Title: Quantitative stability in geometric and functional inequalities\, II\nby Alessio Figalli (ETH) as part of Göran Gustafsson Lectures in Mathe matics\n\n\nAbstract\nGeometric and functional inequalities play a crucial role in several problems arising in analysis and geometry. The issue of t he sharpness of a constant\, as well as the characterization of minimizers \, is a classical and important question. More recently\, there has been a growing interest in studying the stability of such inequalities. The basi c question one wants to address is the following:\n\nSuppose we are given a functional inequality for which minimizers are known. Can we quantitativ ely show that if a function “almost attains the equality\,” then it is close to one of the minimizers?\n\nIn this series of lectures\, I will fi rst give an overview of this beautiful topic and then discuss some recent results concerning the Sobolev\, isoperimetric\, and Brunn–Minkowski ine qualities.\n LOCATION:https://researchseminars.org/talk/GGLectures/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessio Figalli (ETH) DTSTART:20210526T120000Z DTEND:20210526T130000Z DTSTAMP:20260422T212553Z UID:GGLectures/3 DESCRIPTION:Title: Quantitative stability in geometric and functional inequalities\, III\nby Alessio Figalli (ETH) as part of Göran Gustafsson Lectures in Math ematics\n\n\nAbstract\nGeometric and functional inequalities play a crucia l role in several problems arising in analysis and geometry. The issue of the sharpness of a constant\, as well as the characterization of minimizer s\, is a classical and important question. More recently\, there has been a growing interest in studying the stability of such inequalities. The bas ic question one wants to address is the following:\n\nSuppose we are given a functional inequality for which minimizers are known. Can we quantitati vely show that if a function “almost attains the equality\,” then it i s close to one of the minimizers?\n\nIn this series of lectures\, I will f irst give an overview of this beautiful topic and then discuss some recent results concerning the Sobolev\, isoperimetric\, and Brunn–Minkowski in equalities.\n LOCATION:https://researchseminars.org/talk/GGLectures/3/ END:VEVENT BEGIN:VEVENT SUMMARY:June Huh (Princeton) DTSTART:20220530T080000Z DTEND:20220530T090000Z DTSTAMP:20260422T212553Z UID:GGLectures/4 DESCRIPTION:Title: Lorentzian polynomials\nby June Huh (Princeton) as part of Göran G ustafsson Lectures in Mathematics\n\nLecture held in Oskar Klein Auditoriu m FR4\, Albanova\, Roslagstullsbacken 21.\n\nAbstract\nLorentzian polynomi als link continuous convex analysis and discrete convex analysis via tropi cal geometry. The tropical connection is used to produce Lorentzian polyno mials from discrete convex functions. The talk will be accessible to a gen eral audience: No specific background beyond linear algebra and multivaria ble calculus are required for most of the presentation. In addition\, I ad vertise the talk to people with interests in at least one of the following topics: graphs\, convex bodies\, stable polynomials\, projective varietie s\, partition functions\, tropicalizations\, Schur polynomials\, highest w eight representations. Based on joint work with Petter Brändén.\n LOCATION:https://researchseminars.org/talk/GGLectures/4/ END:VEVENT BEGIN:VEVENT SUMMARY:June Huh (Princeton) DTSTART:20220531T074500Z DTEND:20220531T084500Z DTSTAMP:20260422T212553Z UID:GGLectures/5 DESCRIPTION:Title: Open problems on Lorentzian polynomials\nby June Huh (Princeton) as part of Göran Gustafsson Lectures in Mathematics\n\nLecture held in Wall enbergsalen\, Kuskvillan\, Institut Mittag-Leffler.\n\nAbstract\nConjectur ally\, skew-Schur polynomials\, Schur P polynomials\, Schubert polynomials \, homogeneous components of Grothendieck polynomials\, key polynomials\, and homogenized basis generating functions of morphisms of matroids all be come Lorentzian after normalizations. I will present these and some other open problems on Lorentzian polynomials. Joint work with Jacob Matherne\, Karola Mészáros\, and Avery St. Dizier\, and with Chris Eur.\n LOCATION:https://researchseminars.org/talk/GGLectures/5/ END:VEVENT BEGIN:VEVENT SUMMARY:June Huh (Princeton) DTSTART:20220601T074500Z DTEND:20220601T084500Z DTSTAMP:20260422T212553Z UID:GGLectures/6 DESCRIPTION:Title: Kazhdan–Lusztig theory and Hodge theory for matroids\nby June Huh (Princeton) as part of Göran Gustafsson Lectures in Mathematics\n\nLectu re held in Wallenbergsalen\, Kuskvillan\, Institut Mittag-Leffler.\n\nAbst ract\nWe explore the Hodge theory behind the fact that the basis generatin g polynomial of a matroid is Lorentzian. The story reveals a remarkable pa rallel between the theory of Coxeter groups (think of the symmetric group or the dihedral group) and matroids (think of your favorite graph or vecto r configuration). After giving an overview of the similarity\, I will outl ine proofs of two combinatorial conjectures\, the nonnegativity conjecture for Kazhdan–Lusztig polynomials of matroids and the top-heavy conjectur e for the number of flats of matroids. The key step is to formulate and pr ove an analogue of the decomposition theorem in a combinatorial setup. The talk will be accessible to graduate students. Joint work with Tom Braden\ , Jacob Matherne\, Nick Proudfoot\, and Botong Wang.\n LOCATION:https://researchseminars.org/talk/GGLectures/6/ END:VEVENT END:VCALENDAR