[geometry-ml:05731] Dumitrescu氏の講演

[Takuro Mochizuki]

皆様

重複して受け取られた方はご容赦ください。

以前にもお伝えしましたが、
6月12日と6月19日に数理解析研究所本館206号室において、
Olivia Dumitrescu氏による講演が行われます。
タイトル、アブストラクト、日程等については下記をご覧ください。

以前の告知内容とは変更点がございます。
6月12日に予定されていた講演は6月19日に延期されました。
6月12日は6月5日の講演の続きが行われますのでご注意ください。

皆様のご参加をお待ちしています。

京都大学数理解析研究所
望月拓郎

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Title: Interplay between Higgs bundles, opers and quantum curves

Date: June 12 (Wed), 10:00--12:00, 2024

Place: Room 206 RIMS

Speaker: Olivia Dumitrescu (University of North Carolina, Chapel Hill)

Abstract:
The rainbow is one of the most beautiful phenomena in nature. It has inspired art, mythology, and has been a pleasure and challenge to the mathematical physicists for centuries. You might have wondered what awaited you if you went over the rainbow. Is the world on the other side of the rainbow the same as what we know? Sir George Airy discovered the rainbow integral and explained the classical analysis of rainbows, 150 years later, Kontsevich related it to intersections numbers on moduli spaces of punctured Riemann surfaces. These stories are a simple example of a mathematical theory of "quantum curves." I will further continue the exposition and I will present a general framework of quantum curves and I will relate it to topological recursion and the Gaiotto conformal limits that appeared in the previous talks. I will illustrate main differences between the two diffeomorphic moduli spaces, the Hitchin and the de Rham moduli spaces, in terms of lagrangians filling up the ent!
 ire space in rank 2 and rank 1.

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Title: Cones of Curves Stratification

Date: June 19 (Wed), 10:00--12:00, 2024

Place: Room 206 RIMS

Speaker: Olivia Dumitrescu (University of North Carolina, Chapel Hill)

Abstract:
The study of curves in projective space is a well-known problem in algebraic geometry, that goes back centuries. The minimal model program in birational geometry has been formulated via the theory of divisors, and it is an interesting question to understand it via the theory of curves.

In this talk, we discuss the polyhedrality of the cones of divisors ample in codimension k on a Mori dream space and the duality between such cones and the cones of k-moving curves by means of the Mori chamber decomposition of the former. This is based on joint work with Chiara Brambilla, Elisa Postinghel and Luis Santana Sanchez.


-- 
MOCHIZUKI Takuro <takuro ＠ kurims.kyoto-u.ac.jp>