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:20260404T092654Z UID:GGLectures/1 DESCRIPTION:Title: Quantitative stability in geometric and functional inequalities\ , I\nby Alessio Figalli (ETH) as part of Göran Gustafsson Lectures in Mathematics\n\n\nAbstract\nGeometric and functional inequalities play a c rucial role in several problems arising in analysis and geometry. The issu e of the sharpness of a constant\, as well as the characterization of mini mizers\, is a classical and important question. More recently\, there has been a growing interest in studying the stability of such inequalities. Th e basic question one wants to address is the following:\n\nSuppose we are given a functional inequality for which minimizers are known. Can we quant itatively 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 w ill first give an overview of this beautiful topic and then discuss some r ecent results concerning the Sobolev\, isoperimetric\, and Brunn–Minkows ki inequalities.\n LOCATION:https://stable.researchseminars.org/talk/GGLectures/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessio Figalli (ETH) DTSTART:20210525T120000Z DTEND:20210525T130000Z DTSTAMP:20260404T092654Z UID:GGLectures/2 DESCRIPTION:Title: Quantitative stability in geometric and functional inequalities\ , II\nby Alessio Figalli (ETH) as part of Göran Gustafsson Lectures i n Mathematics\n\n\nAbstract\nGeometric and functional inequalities play a crucial role in several problems arising in analysis and geometry. The iss ue of the sharpness of a constant\, as well as the characterization of min imizers\, is a classical and important question. More recently\, there has been a growing interest in studying the stability of such inequalities. T he basic question one wants to address is the following:\n\nSuppose we are given a functional inequality for which minimizers are known. Can we quan titatively show that if a function “almost attains the equality\,” the n it is close to one of the minimizers?\n\nIn this series of lectures\, I will first give an overview of this beautiful topic and then discuss some recent results concerning the Sobolev\, isoperimetric\, and Brunn–Minkow ski inequalities.\n LOCATION:https://stable.researchseminars.org/talk/GGLectures/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessio Figalli (ETH) DTSTART:20210526T120000Z DTEND:20210526T130000Z DTSTAMP:20260404T092654Z UID:GGLectures/3 DESCRIPTION:Title: Quantitative stability in geometric and functional inequalities\ , III\nby Alessio Figalli (ETH) as part of Göran Gustafsson Lectures in Mathematics\n\n\nAbstract\nGeometric and functional inequalities play a crucial role in several problems arising in analysis and geometry. The is sue of the sharpness of a constant\, as well as the characterization of mi nimizers\, is a classical and important question. More recently\, there ha s been a growing interest in studying the stability of such inequalities. The basic question one wants to address is the following:\n\nSuppose we ar e given a functional inequality for which minimizers are known. Can we qua ntitatively show that if a function “almost attains the equality\,” th en it is close to one of the minimizers?\n\nIn this series of lectures\, I will first give an overview of this beautiful topic and then discuss some recent results concerning the Sobolev\, isoperimetric\, and Brunn–Minko wski inequalities.\n LOCATION:https://stable.researchseminars.org/talk/GGLectures/3/ END:VEVENT BEGIN:VEVENT SUMMARY:June Huh (Princeton) DTSTART:20220530T080000Z DTEND:20220530T090000Z DTSTAMP:20260404T092654Z UID:GGLectures/4 DESCRIPTION:Title: Lorentzian polynomials\nby June Huh (Princeton) as part of G öran Gustafsson Lectures in Mathematics\n\nLecture held in Oskar Klein Au ditorium FR4\, Albanova\, Roslagstullsbacken 21.\n\nAbstract\nLorentzian p olynomials link continuous convex analysis and discrete convex analysis vi a tropical geometry. The tropical connection is used to produce Lorentzian polynomials from discrete convex functions. The talk will be accessible t o a general audience: No specific background beyond linear algebra and mul tivariable calculus are required for most of the presentation. In addition \, I advertise the talk to people with interests in at least one of the fo llowing topics: graphs\, convex bodies\, stable polynomials\, projective v arieties\, partition functions\, tropicalizations\, Schur polynomials\, hi ghest weight representations. Based on joint work with Petter Brändén.\n LOCATION:https://stable.researchseminars.org/talk/GGLectures/4/ END:VEVENT BEGIN:VEVENT SUMMARY:June Huh (Princeton) DTSTART:20220531T074500Z DTEND:20220531T084500Z DTSTAMP:20260404T092654Z UID:GGLectures/5 DESCRIPTION:Title: Open problems on Lorentzian polynomials\nby June Huh (Prince ton) as part of Göran Gustafsson Lectures in Mathematics\n\nLecture held in Wallenbergsalen\, Kuskvillan\, Institut Mittag-Leffler.\n\nAbstract\nCo njecturally\, skew-Schur polynomials\, Schur P polynomials\, Schubert poly nomials\, homogeneous components of Grothendieck polynomials\, key polynom ials\, and homogenized basis generating functions of morphisms of matroids all become Lorentzian after normalizations. I will present these and some other open problems on Lorentzian polynomials. Joint work with Jacob Math erne\, Karola Mészáros\, and Avery St. Dizier\, and with Chris Eur.\n LOCATION:https://stable.researchseminars.org/talk/GGLectures/5/ END:VEVENT BEGIN:VEVENT SUMMARY:June Huh (Princeton) DTSTART:20220601T074500Z DTEND:20220601T084500Z DTSTAMP:20260404T092654Z UID:GGLectures/6 DESCRIPTION:Title: Kazhdan–Lusztig theory and Hodge theory for matroids\nby J une Huh (Princeton) as part of Göran Gustafsson Lectures in Mathematics\n \nLecture held in Wallenbergsalen\, Kuskvillan\, Institut Mittag-Leffler.\ n\nAbstract\nWe explore the Hodge theory behind the fact that the basis ge nerating polynomial of a matroid is Lorentzian. The story reveals a remark able parallel between the theory of Coxeter groups (think of the symmetric group or the dihedral group) and matroids (think of your favorite graph o r vector configuration). After giving an overview of the similarity\, I wi ll outline proofs of two combinatorial conjectures\, the nonnegativity con jecture for Kazhdan–Lusztig polynomials of matroids and the top-heavy co njecture for the number of flats of matroids. The key step is to formulate and prove an analogue of the decomposition theorem in a combinatorial set up. The talk will be accessible to graduate students. Joint work with Tom Braden\, Jacob Matherne\, Nick Proudfoot\, and Botong Wang.\n LOCATION:https://stable.researchseminars.org/talk/GGLectures/6/ END:VEVENT END:VCALENDAR