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, 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:

Gromov-Witten invariants
-Definition, examples via algebraic geometry I
-Definition, examples via algebraic geometry II
-Virtual Fundamental Class I (definition)
-Virtual Fundamental Class II (computation in some cases)
Computing GW invariants
-Three level GW classes
-Genus zero invariants of the projective plane
-Genus zero invariants of Calabi-Yau threefolds
Quantum Cohomology 
-Small Quantum Cohomology (Definition and Properties) I
-Small Quantum Cohomology (Definition and Properties) II
-Big Quantum Cohomology I
-Big Quantum Cohomology II
-GW potential
-WDVV equation
GW invariants via Qunatum Cohomology
-The P^2 case
-The Quintic threefold case
-Dubrovin (quantum) connection
Nakajima varieties
-Algebraic and symplectic reduction
-Nakajima Quiver varieties
-Quasi maps to Nakajima varieties
Quantum cohomology of Nakajima varieties 
-Stable envelops and R-matrices I
-Stable envelops and R-matrices II
-Stable envelops and R-matrices III
Yangians I
Yangians II
-Quantum multiplication
-Shift and Quantum operators
-Quantum multiplication by divisors
-Quantum cohomology of cotangent bundle of Grassmannians I, II
Final remarks

 

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