Quantum Cohomology, Nakajima Varieties and Quantum groups

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
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.

Gromov-Witten invariants

Definition, examples via algebraic geometry II

Gromov-Witten invariants

Virtual Fundamental Class I (definition)

Video / Audio / Combined


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

No Lecture
No Lecture
Gromov-Witten invariants

Virtual Fundamental Class II (computation in some cases)

Computing GW invariants

Three level GW classes

Genus zero invariants of the projective plane

Quantum Cohomology

Small Quantum Cohomology (Definition and Properties) I

Quantum Cohomology

Small Quantum Cohomology (Definition and Properties) II

Quantum Cohomology

Big Quantum Cohomology I

Quantum Cohomology

Big Quantum Cohomology II

GW potential

WDVV equation

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

Stable envelops and R-matrices I

Quantum cohomology of Nakajima varieties

Stable envelops and R-matrices II

Quantum cohomology of Nakajima varieties

Stable envelops and R-matrices III

Quantum cohomology of Nakajima varieties

Yangians I

 
Quantum cohomology of Nakajima varieties

Yangians II

No Lecture
No Lecture
Quantum cohomology of Nakajima varieties

Quantum multiplication

Quantum cohomology of Nakajima varieties

Shift and Quantum operators

Quantum cohomology of Nakajima varieties

Quantum multiplication by divisors

Quantum cohomology of Nakajima varieties

Quantum cohomology of cotangent bundle of Grassmannians I, II

Final Remarks

 

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