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This is a periodic series learning seminar organized by Koji Shimizu and Shizhang Li on prismatic F-gauges held on each Monday at MCM110. More info can be found on the website.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Syntomic cohomology in characteristic p
特征p 同调 Syntomic cohomology
2023/4/13
Discuss [Bha, §4.4-4.5]. One reasonable plan is to focus on §4.5 and use it as motivation to introduce materials in §4.4.
This is a periodic series learning seminar organized by Koji Shimizu and Shiz...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Twisted Real quasi-elliptic cohomology
扭曲 实拟椭圆 上同调
2023/4/13
Quasi-elliptic cohomology is closely related to Tate K-theory. It is constructed as an object both reflecting the geometric nature of elliptic curves and more practicable to study than most elliptic c...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Two Approaches towards elliptic cohomology
椭圆 上同调 两种方法
2023/4/14
An elliptic cohomology theory is an even periodic multiplicative generalized cohomology theory whose associated formal group is the formal completion of an elliptic curve. It is at the intersection of...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The de Rham cohomology of p-adic formal schemes
p-adic形式方案 德拉姆 上同调
2023/4/18
Discuss [Bha, §2.5-2.6]. Introduce objects in Definitions 2.5.1 and 2.5.3, and cover Theorem 2.5.6, Corollary 2.5.10, Corollary 2.6.8, and Corollary 2.6.11
This is a periodic series learning seminar ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The de Rham cohomology in characteristic 0
特征0 德拉姆 上同调
2023/4/19
Discuss [Bha, §2.3-2.4]. See [Dri20, §1.3] for the notion of cones and quasi-ideals. Note that some of the remarks (e.g. Remark 2.2.15) [Bha, §2.2] may not have been covered in Lecture 1. Explain them...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Syntomic cohomology and (φ, Γ)-modules
同调 上同调 （φ，Γ）模块
2023/4/26
The goal of this talk is to compare the local Fontaine–Messing period map and the Lazard type period map [CN17, Thm. 4.16]. Since the notation for the general case is too heavy, you may focus on d = 1...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Pro-étale cohomology of affine spaces
仿射空间 亲上同调 [LB18， §3]
2023/5/6
Cover [LB18, §3]. If possible, comment on another proof [CN20].
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On Deligne-Beilinson cohomology of the universal K3 surface
泛K3曲面 Deligne-Beilinson 同调
2023/5/15
O'Grady's generalized Franchetta conjecture is concerned with algebraic cycles of codimension 2 on the universal polarized K3 surface of genus g. This conjecture has been confirmed only for certain sm...
THE PUZZLE CONJECTURE FOR THE COHOMOLOGY OF TWO-STEP FLAG MANIFOLDS
PUZZLE CONJECTURE TWO-STEP FLAG MANIFOLDS
2015/12/17
We prove a conjecture of Knutson asserting that the Schubert
structure constants of the cohomology ring of a two-step flag variety are equal
to the number of puzzles with specified borde...
QUANTUM COHOMOLOGY OF THE LAGRANGIAN GRASSMANNIAN
LAGRANGIAN GRASSMANNIAN QUANTUM COHOMOLOGY
2015/12/17
Let V be a symplectic vector space and LG be the Lagrangian
Grassmannian which parametrizes maximal isotropic subspaces in V . We give
a presentation for the (small) quantum cohomology ring QH¤(LG) ...
QUANTUM COHOMOLOGY OF ORTHOGONAL GRASSMANNIANS
ORTHOGONAL GRASSMANNIANS QUANTUM COHOMOLOGY
2015/12/17
Let V be a vector space with a nondegenerate symmetric form and
OG be the orthogonal Grassmannian which parametrizes maximal isotropic
subspaces in V . We give a presentation for the (small) quantum...
GROMOV-WITTEN INVARIANTS AND QUANTUM COHOMOLOGY OF GRASSMANNIANS
GROMOV-WITTEN INVARIANTS QUANTUM COHOMOLOGY
2015/12/17
This is the written version of my ˉve lectures at the Banach Center
mini-school on `Schubert Varieties', in Warsaw, Poland, May 18{22, 2003.
Let G be a classical Lie group and P a maximal parabolic subgroup. We describe a quantum Pieri rule which holds in the small quantum
cohomology ring of G=P. We also give a presentation of this ring i...
COHOMOLOGY OF SL(2, C) CHARACTER VARIETIES OF SURFACE GROUPS AND THE ACTION OF THE TORELLI GROUP
SL(2, C) CHARACTER VARIETIES SURFACE GROUPS TORELLI GROUP
2015/12/17
We determine the action of the Torelli group on the equivariant cohomology of the space of flat SL(2, C) connections on a closed Riemann surface. We show that the trivial part of the action contains t...