BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ana Maria Castravet (Versailles) DTSTART:20210726T130000Z DTEND:20210726T135000Z DTSTAMP:20260419T093151Z UID:LMSBathSchoolCombAlgGeom/1 DESCRIPTION:Title: Lecture 1: Birational geometry of moduli spaces of ration al curves\nby Ana Maria Castravet (Versailles) as part of LMS-Bath Sum mer School on Combinatorial Algebraic Geometry\n\n\nAbstract\nThe Grothend ieck-Knudsen moduli space of stable\, $n$-pointed rational curves is a fas cinating object. On one hand\, it is a building block towards moduli space s of stable curves of arbitrary genus. On the other hand\, its stratificat ion makes it resemble toric varieties\, which begs the question: to what e xtent is its geometry similar to the geometry of toric varieties?\n\nIn th is series of lectures\, I will explain how the Grothendieck–Knudsen modu li space is in fact similar to the blow-up of a toric variety at the ident ity point. In particular\, I will discuss the case of toric surfaces blown up at a point. An application will be the recent result (joint with Lafac e\, Tevelev\, Ugaglia 2020) that the cone of effective divisors of the Gro thendieck–Knudsen moduli space is not rational polyhedral when $n \\ge 1 0$\, both on characteristic zero and in characteristic $p$\, for an infini te set of primes $p$ of positive density.\n LOCATION:https://researchseminars.org/talk/LMSBathSchoolCombAlgGeom/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ilten (Simon Fraser) DTSTART:20210726T150000Z DTEND:20210726T155000Z DTSTAMP:20260419T093151Z UID:LMSBathSchoolCombAlgGeom/2 DESCRIPTION:Title: Lecture 1: Tangency and tropical geometry\nby Nathan Ilten (Simon Fraser) as part of LMS-Bath Summer School on Combinatorial Al gebraic Geometry\n\n\nAbstract\nIn algebraic geometry\, tangency places an important role in many classical constructions\, including projective dua lity\, tangential varieties\, and theta characteristics. Tropical geometry is a powerful set of tools providing a combinatorial shadow of algebraic geometry. How can we use tools from tropical geometry to study tangency? I will begin this series of lectures by discussing some elements of classic al algebraic geometry related to tangency\, and by introducing basic conce pts of tropical geometry. I will then discuss how tropical geometry can be used to gain information about dual and tangential varieties\, especially in the case of curves. Much of what I discuss will be joint work with Yoa v Len.\n LOCATION:https://researchseminars.org/talk/LMSBathSchoolCombAlgGeom/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Eur (Stanford) DTSTART:20210727T150000Z DTEND:20210727T155000Z DTSTAMP:20260419T093151Z UID:LMSBathSchoolCombAlgGeom/3 DESCRIPTION:Title: Lecture 1: Geometric models of matroids\nby Chris Eur (Stanford) as part of LMS-Bath Summer School on Combinatorial Algebraic G eometry\n\n\nAbstract\nMatroids are combinatorial abstractions of hyperpla ne arrangements\, and admit several geometric models for studying them. W e will survey some recent developments arising from different geometric mo dels of matroids through the lens of tropical and toric geometry. Time pe rmitting\, we will study a new geometric framework that unifies and extend s these recent developments\, and discuss some future directions.\n LOCATION:https://researchseminars.org/talk/LMSBathSchoolCombAlgGeom/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Ana Maria Castravet (Versailles) DTSTART:20210729T130000Z DTEND:20210729T135000Z DTSTAMP:20260419T093151Z UID:LMSBathSchoolCombAlgGeom/4 DESCRIPTION:Title: Lecture 2: Birational geometry of moduli spaces of ration al curves\nby Ana Maria Castravet (Versailles) as part of LMS-Bath Sum mer School on Combinatorial Algebraic Geometry\n\n\nAbstract\nThe Grothend ieck-Knudsen moduli space of stable\, $n$-pointed rational curves is a fas cinating object. On one hand\, it is a building block towards moduli space s of stable curves of arbitrary genus. On the other hand\, its stratificat ion makes it resemble toric varieties\, which begs the question: to what e xtent is its geometry similar to the geometry of toric varieties?\n\nIn th is series of lectures\, I will explain how the Grothendieck–Knudsen modu li space is in fact similar to the blow-up of a toric variety at the ident ity point. In particular\, I will discuss the case of toric surfaces blown up at a point. An application will be the recent result (joint with Lafac e\, Tevelev\, Ugaglia 2020) that the cone of effective divisors of the Gro thendieck–Knudsen moduli space is not rational polyhedral when $n \\ge 1 0$\, both on characteristic zero and in characteristic $p$\, for an infini te set of primes $p$ of positive density.\n LOCATION:https://researchseminars.org/talk/LMSBathSchoolCombAlgGeom/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Eur (Stanford) DTSTART:20210729T150000Z DTEND:20210729T155000Z DTSTAMP:20260419T093151Z UID:LMSBathSchoolCombAlgGeom/5 DESCRIPTION:Title: Lecture 2: Geometric models of matroids\nby Chris Eur (Stanford) as part of LMS-Bath Summer School on Combinatorial Algebraic G eometry\n\n\nAbstract\nMatroids are combinatorial abstractions of hyperpla ne arrangements\, and admit several geometric models for studying them. W e will survey some recent developments arising from different geometric mo dels of matroids through the lens of tropical and toric geometry. Time pe rmitting\, we will study a new geometric framework that unifies and extend s these recent developments\, and discuss some future directions.\n LOCATION:https://researchseminars.org/talk/LMSBathSchoolCombAlgGeom/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ilten (Simon Fraser) DTSTART:20210730T150000Z DTEND:20210730T155000Z DTSTAMP:20260419T093151Z UID:LMSBathSchoolCombAlgGeom/6 DESCRIPTION:Title: Lecture 2: Tangency and tropical geometry\nby Nathan Ilten (Simon Fraser) as part of LMS-Bath Summer School on Combinatorial Al gebraic Geometry\n\n\nAbstract\nIn algebraic geometry\, tangency places an important role in many classical constructions\, including projective dua lity\, tangential varieties\, and theta characteristics. Tropical geometry is a powerful set of tools providing a combinatorial shadow of algebraic geometry. How can we use tools from tropical geometry to study tangency? I will begin this series of lectures by discussing some elements of classic al algebraic geometry related to tangency\, and by introducing basic conce pts of tropical geometry. I will then discuss how tropical geometry can be used to gain information about dual and tangential varieties\, especially in the case of curves. Much of what I discuss will be joint work with Yoa v Len.\n LOCATION:https://researchseminars.org/talk/LMSBathSchoolCombAlgGeom/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Ana Maria Castravet (Versailles) DTSTART:20210802T130000Z DTEND:20210802T135000Z DTSTAMP:20260419T093151Z UID:LMSBathSchoolCombAlgGeom/7 DESCRIPTION:Title: Lecture 3: Birational geometry of moduli spaces of ration al curves\nby Ana Maria Castravet (Versailles) as part of LMS-Bath Sum mer School on Combinatorial Algebraic Geometry\n\n\nAbstract\nThe Grothend ieck-Knudsen moduli space of stable\, $n$-pointed rational curves is a fas cinating object. On one hand\, it is a building block towards moduli space s of stable curves of arbitrary genus. On the other hand\, its stratificat ion makes it resemble toric varieties\, which begs the question: to what e xtent is its geometry similar to the geometry of toric varieties?\n\nIn th is series of lectures\, I will explain how the Grothendieck–Knudsen modu li space is in fact similar to the blow-up of a toric variety at the ident ity point. In particular\, I will discuss the case of toric surfaces blown up at a point. An application will be the recent result (joint with Lafac e\, Tevelev\, Ugaglia 2020) that the cone of effective divisors of the Gro thendieck–Knudsen moduli space is not rational polyhedral when $n \\ge 1 0$\, both on characteristic zero and in characteristic $p$\, for an infini te set of primes $p$ of positive density.\n LOCATION:https://researchseminars.org/talk/LMSBathSchoolCombAlgGeom/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ilten (Simon Fraser) DTSTART:20210802T150000Z DTEND:20210802T155000Z DTSTAMP:20260419T093151Z UID:LMSBathSchoolCombAlgGeom/8 DESCRIPTION:Title: Lecture 3: Tangency and tropical geometry\nby Nathan Ilten (Simon Fraser) as part of LMS-Bath Summer School on Combinatorial Al gebraic Geometry\n\n\nAbstract\nIn algebraic geometry\, tangency places an important role in many classical constructions\, including projective dua lity\, tangential varieties\, and theta characteristics. Tropical geometry is a powerful set of tools providing a combinatorial shadow of algebraic geometry. How can we use tools from tropical geometry to study tangency? I will begin this series of lectures by discussing some elements of classic al algebraic geometry related to tangency\, and by introducing basic conce pts of tropical geometry. I will then discuss how tropical geometry can be used to gain information about dual and tangential varieties\, especially in the case of curves. Much of what I discuss will be joint work with Yoa v Len.\n LOCATION:https://researchseminars.org/talk/LMSBathSchoolCombAlgGeom/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Eur (Stanford) DTSTART:20210803T150000Z DTEND:20210803T155000Z DTSTAMP:20260419T093151Z UID:LMSBathSchoolCombAlgGeom/9 DESCRIPTION:Title: Lecture 3: Geometric models of matroids\nby Chris Eur (Stanford) as part of LMS-Bath Summer School on Combinatorial Algebraic G eometry\n\n\nAbstract\nMatroids are combinatorial abstractions of hyperpla ne arrangements\, and admit several geometric models for studying them. W e will survey some recent developments arising from different geometric mo dels of matroids through the lens of tropical and toric geometry. Time pe rmitting\, we will study a new geometric framework that unifies and extend s these recent developments\, and discuss some future directions.\n LOCATION:https://researchseminars.org/talk/LMSBathSchoolCombAlgGeom/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Ilten (Simon Fraser) DTSTART:20210804T150000Z DTEND:20210804T155000Z DTSTAMP:20260419T093151Z UID:LMSBathSchoolCombAlgGeom/10 DESCRIPTION:Title: Lecture 4: Tangency and tropical geometry\nby Nathan Ilten (Simon Fraser) as part of LMS-Bath Summer School on Combinatorial A lgebraic Geometry\n\n\nAbstract\nIn algebraic geometry\, tangency places a n important role in many classical constructions\, including projective du ality\, tangential varieties\, and theta characteristics. Tropical geometr y is a powerful set of tools providing a combinatorial shadow of algebraic geometry. How can we use tools from tropical geometry to study tangency? I will begin this series of lectures by discussing some elements of classi cal algebraic geometry related to tangency\, and by introducing basic conc epts of tropical geometry. I will then discuss how tropical geometry can b e used to gain information about dual and tangential varieties\, especiall y in the case of curves. Much of what I discuss will be joint work with Yo av Len.\n LOCATION:https://researchseminars.org/talk/LMSBathSchoolCombAlgGeom/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Ana Maria Castravet (Versailles) DTSTART:20210806T130000Z DTEND:20210806T135000Z DTSTAMP:20260419T093151Z UID:LMSBathSchoolCombAlgGeom/11 DESCRIPTION:Title: Lecture 4: Birational geometry of moduli spaces of ratio nal curves\nby Ana Maria Castravet (Versailles) as part of LMS-Bath Su mmer School on Combinatorial Algebraic Geometry\n\n\nAbstract\nThe Grothen dieck-Knudsen moduli space of stable\, $n$-pointed rational curves is a fa scinating object. On one hand\, it is a building block towards moduli spac es of stable curves of arbitrary genus. On the other hand\, its stratifica tion makes it resemble toric varieties\, which begs the question: to what extent is its geometry similar to the geometry of toric varieties?\n\nIn t his series of lectures\, I will explain how the Grothendieck–Knudsen mod uli space is in fact similar to the blow-up of a toric variety at the iden tity point. In particular\, I will discuss the case of toric surfaces blow n up at a point. An application will be the recent result (joint with Lafa ce\, Tevelev\, Ugaglia 2020) that the cone of effective divisors of the Gr othendieck–Knudsen moduli space is not rational polyhedral when $n \\ge 10$\, both on characteristic zero and in characteristic $p$\, for an infin ite set of primes $p$ of positive density.\n LOCATION:https://researchseminars.org/talk/LMSBathSchoolCombAlgGeom/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Eur (Stanford) DTSTART:20210806T150000Z DTEND:20210806T155000Z DTSTAMP:20260419T093151Z UID:LMSBathSchoolCombAlgGeom/12 DESCRIPTION:Title: Lecture 4: Geometric models of matroids\nby Chris Eu r (Stanford) as part of LMS-Bath Summer School on Combinatorial Algebraic Geometry\n\n\nAbstract\nMatroids are combinatorial abstractions of hyperpl ane arrangements\, and admit several geometric models for studying them. We will survey some recent developments arising from different geometric m odels of matroids through the lens of tropical and toric geometry. Time p ermitting\, we will study a new geometric framework that unifies and exten ds these recent developments\, and discuss some future directions.\n LOCATION:https://researchseminars.org/talk/LMSBathSchoolCombAlgGeom/12/ END:VEVENT END:VCALENDAR