September 22, 2010, 11:30 am

Here are my notes from Manivel’s talk in Bonn:

Manivel_Bonn_Sep_2010

Summary:

- geometric Satake after Drinfeld and Ginzburg
- example:
- the quantum Chevalley formula (Fulton–Woodward)
- cohomology of G/P in general
- cohomology of G/P: improvements in the miniscule case
- semisimplicity of (Chaput–Manivel–Perrin) and connections to work of Kostant (Gorbunov–Petrov)
- quantum Satake for miniscule type-D Grassmannians

September 22, 2010, 11:23 am

Here are my notes from Golyshev’s second talk in Bonn:

Golyshev_2_Bonn_Sep_2010

Summary:

- the “spin representation of K3” and its quantum analog
- some evidence: the Bertram–Ciocan-Fontanine–Kim result for
- the geometric Satake correspondence (Drinfeld–Ginzburg)
- miniscule Grassmannians as smooth -orbits in the affine Grassmannian
- a quantum analog of geometric Satake in this case

September 22, 2010, 11:17 am

Here are my notes from Kresch’s talk in Bonn:

Kresch_Bonn_Sep_2010

Summary:

- the orthogonal Grassmannian
- Schubert varieties are indexed by strict partitions
- special Schubert classes
- ring presentations for and
- the connection to algebraic combinatorics via Praguez-Rataiski polynomials
- quantum Giambelli and quantum Pieri (Kresch-Tamvarkis)

September 22, 2010, 11:13 am

Here are my notes from Katzarkov’s talk in Bonn:

Katzarkov_Bonn_Sep_2010

Summary:

- Clemens-Griffiths showed that the 3-dimensional cubic is not rational by showing that its intermediate Jacobian is not the Jacobian of a curve; we suggest analogs of this.
- Homological Mirror Symmetry and the perverse sheaf of vanishing cycles
- detecting rationality via monodromy properties on the LG mirror (Gross-Katzarkov, Pryzalkowski, Golyshev)
- spectra of triangulated categories; examples
- Theorem: is rational of dimension implies that the spectrum of has no gaps of size greaeter than
- the outlook for 4-dimensional cubics

September 22, 2010, 11:07 am

Here are my notes from Golyshev’s talk in Bonn.

Golyshev_1_Bonn_Sep_2010

Summary:

- a historical analogy: the study of Fano varieties now versus algebraic number theory prior to the proof of the Weil Conjectures
- linearization and motives
- Tannakian categories
- the “quantum Tannakian category”
- realizations in algebraic number theory: one can detect algebraic varieties by detecting their motives (in practice by detecting their L-functions via Selberg-Stark)
- the “quantum Tate realization” and quantum detection
- the Satake correspondence and its quantum parallel