Quantum Cohomology, Nakajima Varieties and Quantum groups

2018-01-25 14:21 - 2018-03-06 14:21

During the Spring 2018 Semester Artan Sheshmani (QGM/CMSA) will be teaching a CMSA special lecture series on Quantum Cohomology, Nakajima Vareties and Quantum groups. The lectures will be held Tuesdays and Thursdays beginning January 25th, from 1:00 to 3:00pm in room G10, CMSA Building.

You can watch Prof. Sheshmani describe the series here.

The Syllabus is as follows:

Date……….. Topic Video/Audio
1-25-2018 Gromov-Witten invariants 

Definition, examples via algebraic geometry I

Video / Audio / Combined 


*due to technical difficulties the audio and video are split for this lecture.

 2-01-2018 Gromov-Witten invariants 

Virtual Fundamental Class I (definition)

Video Audio / Combined 


*due to technical difficulties the audio and video are split for this lecture

2-13-2018 Gromov-Witten invariants 

Virtual Fundamental Class II (computation in some cases)

 2-15-2018 Computing GW invariants 

Three level GW classes

Genus zero invariants of the projective plane

 2-20-2018 Quantum Cohomology 

Small Quantum Cohomology (Definition and Properties) I

2-22-2018 Quantum Cohomology 

Small Quantum Cohomology (Definition and Properties) II

2-27-2018 Quantum Cohomology 

Big Quantum Cohomology I

 3-1-2018 Quantum Cohomology 

Big Quantum Cohomology II

GW potential

WDVV equation

3-6-2018 GW invariants via Quantum Cohomology 

The Quintic threefold case

The P^2 case

GW invariants via Quantum Cohomology 

Dubrovin (quantum) connection

Nakajima varieties 

-Algebraic and symplectic reduction

Nakajima varieties 

Quasi maps to Nakajima varieties

Quantum cohomology of Nakajima varieties 

Small Quantum Cohomology of Hilb^n (C2) I

Quantum cohomology of Nakajima varieties 

Small Quantum Cohomology of Hilb^n (C2) II

Quantum cohomology of Nakajima varieties 

Small Quantum Cohomology of Hilb^n (C2) III

Quantum cohomology of Nakajima varieties 

Big Quantum Cohomology of Hilb^n (C2) I

 
Quantum cohomology of Nakajima varieties 

Big Quantum Cohomology of Hilb^n (C2) II

Quantum cohomology of Nakajima varieties 

Big Quantum Cohomology of Hilb^n (C2) III

Quantum cohomology of Nakajima varieties 

Big Quantum Cohomology of Hilb^n (C2) IV