BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yunhyung Cho (Sungkyunkwan University) DTSTART:20210125T010000Z DTEND:20210125T020000Z DTSTAMP:20260416T114837Z UID:ComFlag2021/1 DESCRIPTION:Title: A brief introduction to toric varieties and Newton-Okounkov bodies II< /a>\nby Yunhyung Cho (Sungkyunkwan University) as part of Combinatorics on flag varieties and related topics 2021\n\n\nAbstract\nThis talk will be a preliminary talk of this workshop and covers the following topics: $\\new line$\n- Introduction to toric varieties (definitions\, structure theorems \, etc..) $\\newline$\n- Sheaves of divisors on toric varieties $\\newlin e$\n- Introduction to Newton-Okounkov bodies: in view of the generalizati on of moment polytopes.\n LOCATION:https://researchseminars.org/talk/ComFlag2021/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Yunhyung Cho (Sungkyunkwan University) DTSTART:20210125T022000Z DTEND:20210125T032000Z DTSTAMP:20260416T114837Z UID:ComFlag2021/2 DESCRIPTION:Title: A brief introduction to toric varieties and Newton-Okounkov bodies I\nby Yunhyung Cho (Sungkyunkwan University) as part of Combinatorics on flag varieties and related topics 2021\n\n\nAbstract\nThis talk will be a preliminary talk of this workshop and covers the following topics: $\\newl ine$\n- Introduction to toric varieties (definitions\, structure theorems\ , etc..) $\\newline$\n- Sheaves of divisors on toric varieties $\\newline $\n- Introduction to Newton-Okounkov bodies: in view of the generalizatio n of moment polytopes.\n LOCATION:https://researchseminars.org/talk/ComFlag2021/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Naoki Fujita (The University of Tokyo) DTSTART:20210125T050000Z DTEND:20210125T060000Z DTSTAMP:20260416T114837Z UID:ComFlag2021/3 DESCRIPTION:Title: Introduction to crystal bases I\nby Naoki Fujita (The University o f Tokyo) as part of Combinatorics on flag varieties and related topics 202 1\n\n\nAbstract\nKashiwara's crystal basis is a combinatorial skeleton of a representation of a semisimple Lie algebra. Through the Borel-Weil theor y\, it relates geometry of flag varieties with combinatorics of tableaux a nd polytopes. In the 1st talk\, we survey the theory of crystal bases in t he case of special linear groups.\n LOCATION:https://researchseminars.org/talk/ComFlag2021/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Naoki Fujita (The University of Tokyo) DTSTART:20210125T062000Z DTEND:20210125T072000Z DTSTAMP:20260416T114837Z UID:ComFlag2021/4 DESCRIPTION:Title: Introduction to crystal bases II\nby Naoki Fujita (The University of Tokyo) as part of Combinatorics on flag varieties and related topics 20 21\n\n\nAbstract\nIn the theory of crystal bases\, it is important to give their concrete realizations. Until now\, many geometric or combinatorial realizations have been discovered. In the 2nd talk\, we discuss some combi natorial realizations using tableaux and polytopes.\n LOCATION:https://researchseminars.org/talk/ComFlag2021/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Lara Bossinger (UNAM Instituto de Matemáticas Unidad Oaxaca) DTSTART:20210126T010000Z DTEND:20210126T020000Z DTSTAMP:20260416T114837Z UID:ComFlag2021/5 DESCRIPTION:Title: Gröbner degenerations of Grassmannains and cluster algebras I\nby Lara Bossinger (UNAM Instituto de Matemáticas Unidad Oaxaca) as part of Combinatorics on flag varieties and related topics 2021\n\n\nAbstract\nMy lectures will be split in two parts: in the first I will explain the clust er structure of Grassmannains and how it allows to construct (toric) degen erations. This part is based on work of Scott from 2006 (who showed that t he homogeneous coordinate ring of the Grassmannian with respect to its Pl ücker embedding is a cluster algebra) and on work of Gross\, Hacking\, Ke el and Kontsevich from 2018 (who showed\, among other things\, how to cons truct toric degenerations of cluster varieties). In the second part of the lectures I will explain how to realize the above mentioned toric degenera tions as Gröbner degenerations. Moreover\, we will see how one particular maximal cone in the Gröbner fan of a Grassmannain (of finite cluster typ e) captures all cluster toric degenerations. The second part is based on w ork of myself from 2020 and a joint preprint with Fatemeh Mohammadi and Al fredo Nájera Chávez from 2020.\n LOCATION:https://researchseminars.org/talk/ComFlag2021/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Lara Bossinger (UNAM Instituto de Matemáticas Unidad Oaxaca) DTSTART:20210126T022000Z DTEND:20210126T032000Z DTSTAMP:20260416T114837Z UID:ComFlag2021/6 DESCRIPTION:Title: Gröbner degenerations of Grassmannains and cluster algebras II\nb y Lara Bossinger (UNAM Instituto de Matemáticas Unidad Oaxaca) as part of Combinatorics on flag varieties and related topics 2021\n\n\nAbstract\nMy lectures will be split in two parts: in the first I will explain the clus ter structure of Grassmannains and how it allows to construct (toric) dege nerations. This part is based on work of Scott from 2006 (who showed that the homogeneous coordinate ring of the Grassmannian with respect to its Pl ücker embedding is a cluster algebra) and on work of Gross\, Hacking\, Ke el and Kontsevich from 2018 (who showed\, among other things\, how to cons truct toric degenerations of cluster varieties). In the second part of the lectures I will explain how to realize the above mentioned toric degenera tions as Gröbner degenerations. Moreover\, we will see how one particular maximal cone in the Gröbner fan of a Grassmannain (of finite cluster typ e) captures all cluster toric degenerations. The second part is based on w ork of myself from 2020 and a joint preprint with Fatemeh Mohammadi and Al fredo Nájera Chávez from 2020.\n LOCATION:https://researchseminars.org/talk/ComFlag2021/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Naoki Fujita (The University of Tokyo) DTSTART:20210126T050000Z DTEND:20210126T060000Z DTSTAMP:20260416T114837Z UID:ComFlag2021/7 DESCRIPTION:Title: Newton-Okounkov bodies of flag and Schubert varieties I\nby Naoki Fujita (The University of Tokyo) as part of Combinatorics on flag varietie s and related topics 2021\n\n\nAbstract\nA Newton-Okounkov body is a conve x body constructed from a projective variety with a globally generated lin e bundle and with a higher rank valuation on the function field\, which gi ves a systematic method of constructing toric degenerations of projective varieties. The notion of Newton-Okounkov bodies was originally introduced to study multiplicity functions for representations of a semisimple group\ , and afterward developed as a generalization of toric theory. In the 3rd talk\, we survey the theory of Newton-Okounkov bodies and its geometric ap plications. In the case of flag and Schubert varieties\, we also discuss r elations between Newton-Okounkov bodies and crystal bases.\n LOCATION:https://researchseminars.org/talk/ComFlag2021/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Naoki Fujita (The University of Tokyo) DTSTART:20210126T062000Z DTEND:20210126T072000Z DTSTAMP:20260416T114837Z UID:ComFlag2021/8 DESCRIPTION:Title: Newton-Okounkov bodies of flag and Schubert varieties II\nby Naoki Fujita (The University of Tokyo) as part of Combinatorics on flag varieti es and related topics 2021\n\n\nAbstract\nFor a specific Newton-Okounkov b ody of a flag variety\, the associated toric degeneration of the flag vari ety induces semi-toric degenerations of (opposite) Schubert varieties. In the 4th talk\, we discuss which Newton-Okounkov bodies have this property. We also see some explicit descriptions of induced semi-toric degeneration s.\n LOCATION:https://researchseminars.org/talk/ComFlag2021/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Megumi Harada (McMaster University) DTSTART:20210127T010000Z DTEND:20210127T015000Z DTSTAMP:20260416T114837Z UID:ComFlag2021/9 DESCRIPTION:Title: An introduction to Hessenberg varieties and their Newton-Okounkov bodi es I\nby Megumi Harada (McMaster University) as part of Combinatorics on flag varieties and related topics 2021\n\n\nAbstract\nThis expository t alk will consist of two parts. The first part will be an introduction to H essenberg varieties and their relation to many other topics such as Schube rt calculus\, representation theory\, the theory of (quasi)symmetric funct ions\, and combinatorics. There is much interesting work in this area\, so this first part will be a "survey" talk\, and I will try to give an overa ll sense of the history and some of the big themes\, instead of spending a lot of time on details. In the second portion of the talk\, I will recou nt what is known about Newton-Okounkov bodies of Hessenberg varieties. In fact\, not very much is known\, so this second part will be shorter\, and more speculative. We will close with some open questions which I hope tha t members of the audience would be interested to answer!\n LOCATION:https://researchseminars.org/talk/ComFlag2021/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Megumi Harada (McMaster University) DTSTART:20210127T020000Z DTEND:20210127T025000Z DTSTAMP:20260416T114837Z UID:ComFlag2021/10 DESCRIPTION:Title: An introduction to Hessenberg varieties and their Newton-Okounkov bod ies II\nby Megumi Harada (McMaster University) as part of Combinatoric s on flag varieties and related topics 2021\n\n\nAbstract\nThis expository talk will consist of two parts. The first part will be an introduction to Hessenberg varieties and their relation to many other topics such as Schu bert calculus\, representation theory\, the theory of (quasi)symmetric fun ctions\, and combinatorics. There is much interesting work in this area\, so this first part will be a "survey" talk\, and I will try to give an ove rall sense of the history and some of the big themes\, instead of spending a lot of time on details. In the second portion of the talk\, I will rec ount what is known about Newton-Okounkov bodies of Hessenberg varieties. In fact\, not very much is known\, so this second part will be shorter\, a nd more speculative. We will close with some open questions which I hope t hat members of the audience would be interested to answer!\n LOCATION:https://researchseminars.org/talk/ComFlag2021/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Akihiro Higashitani (Osaka University) DTSTART:20210127T050000Z DTEND:20210127T060000Z DTSTAMP:20260416T114837Z UID:ComFlag2021/11 DESCRIPTION:Title: Introduction to combinatorial mutations of polytopes and its applicat ions I\nby Akihiro Higashitani (Osaka University) as part of Combinato rics on flag varieties and related topics 2021\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ComFlag2021/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Akihiro Higashitani (Osaka University) DTSTART:20210127T062000Z DTEND:20210127T072000Z DTSTAMP:20260416T114837Z UID:ComFlag2021/12 DESCRIPTION:Title: Introduction to combinatorial mutations of polytopes and its applicat ions II\nby Akihiro Higashitani (Osaka University) as part of Combinat orics on flag varieties and related topics 2021\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ComFlag2021/12/ END:VEVENT END:VCALENDAR