RIT on Geometry and Physics Archives for Academic Year 2021


Organizational meeting for fall 2020

When: Thu, September 10, 2020 - 3:30pm
Where: online, contact Jonathan Rosenberg for zoom link
Speaker: () -
Abstract: The planned topic for 2020 is "tropical geometry" and its applications to physics. A useful source is the book by Mark Gross, http://www.math.ucsd.edu/~mgross/kansas.pdf

Tropical algebra and curves in the plane

When: Thu, September 17, 2020 - 3:30pm
Where: online, contact Jonathan Rosenberg for zoom link
Speaker: Sze-Hong Kwong, UMD-
Abstract: We will start with the first two chapters of "Brief introduction to tropical geometry" by Mikhalkin et al., arXiv:1502.05950

Tropical algebra and curves in the plane (cont'd)

When: Thu, September 24, 2020 - 3:30pm
Where: online, contact Jonathan Rosenberg for zoom link
Speaker: Sze-Hong Kwong, UMD-
Abstract: More on amoebas and curves from "Brief introduction to tropical geometry" by Mikhalkin et al., arXiv:1502.05950

Tropical algebra and applications to real algebraic gometry

When: Thu, October 1, 2020 - 3:30pm
Where: online, contact Jonathan Rosenberg for zoom link
Speaker: Siddharth Taneja, UMD -
Abstract: Chapter 3 of "Brief introduction to tropical geometry" by Mikhalkin et al., arXiv:1502.05950

Introduction to Enumerative Geometry and Gromov-Witten Invariants

When: Thu, October 8, 2020 - 3:30pm
Where: online, contact Jonathan Rosenberg for zoom link
Speaker: Steven Jin, UMD -

Applications of Tropical Geometry to Enumerative Geometry

When: Thu, October 15, 2020 - 3:30pm
Where: online, contact Jonathan Rosenberg for zoom link
Speaker: Steven Jin, UMD -
Abstract: Chapter 4 of "Brief introduction to tropical geometry" by Mikhalkin et al., arXiv:1502.05950

Tropical Homology with Applications to Hodge and K-Theory

When: Thu, October 22, 2020 - 3:30pm
Where: online, contact Jonathan Rosenberg for zoom link
Speaker: Saul Hilsenrath (UMD)
Abstract: Tropical manifolds are polyhedral spaces locally modeled by Bergman fans. Of particular interest are the tropical manifolds which are Hausdorff limits of the tropicalizations (amoebas) of families of projective algebraic varieties, due to the connection between their homology and the Hodge numbers of the algebraic families. In this talk, I will introduce tropical manifolds in terms of Bergman fans of matroids and prove Zharkov’s result relating Bergman fans to Orlik-Solomon algebras. I will then present Itenberg et al.’s tropical homology, followed by Gross and Shokrieh’s sheaf-theoretic perspective. Turning to applications, I will present the proof, using the Steenbrink-Illusie spectral sequence, that the Hodge numbers of a family of projective algebraic varieties equal the dimensions of the homology groups of the family’s tropical limit. Building on this connection with Hodge theory, I will discuss Zharkov and Kontsevich’s tropical Hodge conjecture, followed by Mikami’s tropical Milnor K-theory and the tropical Hodge conjecture it implies. I will conclude with a result by Speyer relating K-theory to an invariant of matroids via tropical linear spaces.

A and B models

When: Thu, October 29, 2020 - 3:30pm
Where: online, contact Jonathan Rosenberg for zoom link
Speaker: Elliot Kienzle (UMD)
Abstract: starting on Gross's book

A and B models

When: Thu, November 5, 2020 - 3:30pm
Where: online, contact Jonathan Rosenberg for zoom link
Speaker: Elliot Kienzle (UMD)
Abstract: starting on Gross's book

The B-model (cont'd) followed by Intro to Log Geometry

When: Thu, November 12, 2020 - 3:30pm
Where: online, contact Jonathan Rosenberg for zoom link
Speaker: Elliot Kienzle and Amin Gholampour (UMD)
Abstract: We will finish up Gross Ch. 2 and then move on to Gross Ch. 3.

Log Geometry

When: Thu, November 19, 2020 - 3:30pm
Where: online, contact Jonathan Rosenberg for zoom link
Speaker: Amin Gholampour (UMD)
Abstract: Gross Ch. 3.

no meeting this week because of schedule conflict

When: Thu, December 3, 2020 - 3:30pm
Where:


Log Geometry

When: Thu, December 10, 2020 - 3:15pm
Where: online, contact Jonathan Rosenberg for zoom link
Speaker: Amin Gholampour (UMD)
Abstract: Gross Ch. 3.

Organizational meeting for spring 2021

When: Thu, January 28, 2021 - 3:30pm
Where: online at Zoom meeting 916 8725 5505, contact Jonathan Rosenberg for passcode
Speaker: () -
Abstract: The planned topic for 2020 is "tropical geometry" and its applications to physics. A useful source is the book by Mark Gross, http://www.math.ucsd.edu/~mgross/kansas.pdf

Review of Gross Chapter 3 on Log Geometry

When: Thu, February 4, 2021 - 3:30pm
Where: online at Zoom meeting 916 8725 5505, contact Jonathan Rosenberg for passcode
Speaker: Amin Gholampour

Relating Log Geometry to the Mikhalkin Theorem

When: Thu, February 11, 2021 - 3:30pm
Where: online at Zoom meeting 916 8725 5505, contact Jonathan Rosenberg for passcode
Speaker: Amin Gholampour

Gross 5.1: Landau-Ginzburg models

When: Thu, February 25, 2021 - 3:30pm
Where: online at Zoom meeting 916 8725 5505, contact Jonathan Rosenberg for passcode
Speaker: Jonathan Rosenberg

Gross 5.2: Tropical descendent invariants

When: Thu, March 4, 2021 - 3:30pm
Where: online at Zoom meeting 916 8725 5505, contact Jonathan Rosenberg for passcode
Speaker: Steven Jin

Gauged Linear Sigma Models and connections to physics

When: Thu, March 11, 2021 - 3:30pm
Where:
Speaker: Tristan Hubsch

Gross 5.3: The main B-model result

When: Thu, March 25, 2021 - 3:30pm
Where:
Speaker: Amin Gholampour

An introduction to the Classical Langlands program

When: Thu, April 1, 2021 - 3:30pm
Where:
Speaker: Steven Jin (UMd)

An Introduction to the (Categorical) Geometric Langlands program

When: Thu, April 8, 2021 - 3:30pm
Where:
Speaker: Steven Jin

Aspects of 4-dimensional gauge theory

When: Thu, April 15, 2021 - 3:30pm
Where:
Speaker: Siddarth Taneja

Mirror symmetry of Hitchin moduli spaces

When: Thu, April 22, 2021 - 3:30pm
Where:
Speaker: Elliot Kienzle

Mirror symmetry of Hitchin moduli spaces

When: Thu, April 29, 2021 - 3:30pm
Where:
Speaker: Elliot Kienzle