# Michael Zhao Memorial Student Colloquium (Spring 2023)

Each week, the Michael Zhao Memorial Student Colloquium holds 45-minute talks by Columbia mathematics faculty about their own research. The talks are intended for current PhD students in mathematics at Columbia. If you are an undergraduate student or external graduate student and would like to come, please email ams2637@columbia.edu or rh3101@columbia.edu.

• When: Tuesday 6:00 - 7:00 PM ET
• Where: Mathematics Building, Room 520
• Organizers:Rafah Hajjar Muñoz, Alex Scheffelin

## Schedule

1/24
None
1/31
Inbar Klang
(Homotopical) fixed point theory
Given a map $$f$$ from a topological space $$X$$ to itself, one can ask whether it has fixed points, and whether it can be modified to remove the fixed points. I will discuss invariants in algebraic topology that answer these questions, the Lefschetz number and the Reidemeister trace. Time permitting, I will briefly discuss variations of this problem (equivariant, or in families), in which homotopy theory becomes very useful.
2/7
Andrew Hanlon
Homological mirror symmetry for projective space
The homological mirror symmetry conjecture aims to relate natural categories in algebraic and symplectic geometry. Namely, it predicts a derived equivalence between the category of coherent sheaves on certain spaces and the Fukaya category on a mirror space. We will discuss aspects of this conjecture and its proof for projective space while pointing out more general principles.
2/14
TBD
TBD
TBD
2/21
TBD
TBD
TBD
2/28
TBD
TBD
TBD
3/7
TBD
TBD
TBD
3/14
Spring Break
3/21
TBD
TBD
TBD
3/28
TBD
TBD
TBD
4/4
TBD
TBD
TBD
4/11
TBD
TBD
TBD
4/18
TBD
TBD
TBD
4/25
TBD
TBD
TBD