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
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.

1-29-2018 Gromov-Witten invariants

Definition, examples via algebraic geometry II

2-1-2018 Gromov-Witten invariants

Virtual Fundamental Class I (definition)

Video / Audio / Combined


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

2-6-2018 No Lecture
2-8-2018 No 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

3-6-2018 Quantum Cohomology

GW potential

3-8-2018 Quantum Cohomology

WDVV equation

3-13-2018 GW invariants via Quantum Cohomology

The P^2 case

3-15-2018 GW invariants via Quantum Cohomology

The Quintic threefold case

3-20-2018 GW invariants via Quantum Cohomology

Dubrovin (quantum) connection

3-22-2018 Nakajima varieties

-Algebraic and symplectic reduction

3-27-2018 Nakajima varieties

Nakajima Quiver varieties

3-29-2018 Nakajima varieties

Quasi maps to Nakajima varieties

4-3-2018 Quantum cohomology of Nakajima varieties

Stable envelops and R-matrices I

4-5-2018 Quantum cohomology of Nakajima varieties

Stable envelops and R-matrices II

4-10-2018 No Lecture
4-12-2018 No Lecture
4-17-2018 Quantum cohomology of Nakajima varieties

Stable envelops and R-matrices III

4-19-2018 Quantum cohomology of Nakajima varieties

Yangians I

4-24-2018 Quantum cohomology of Nakajima varieties

Yangians II

4-26-2018 Quantum cohomology of Nakajima varieties

Quantum multiplication

5-1-2018 Quantum cohomology of Nakajima varieties

Shift and Quantum operators

5-3-2018 Quantum cohomology of Nakajima varieties

Quantum multiplication by divisors

5-8-2018 Quantum cohomology of Nakajima varieties

Quantum cohomology of cotangent bundle of Grassmannians I, II

5-10-2018 Final Remarks

 

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