Sample Notes from Previous Talks



General Audience Talk. Claremont McKenna College Summer Research Program (SRP) 


"Review of Differential Geometry." Claremont Consortium Analysis Seminar. Notes from Chapter 1 of Mirror Symmetry by Hori-Katz-Klemm-Pandharipande-Thomas-Vafa-Vakil-Zaslow.

"Homological Mirror Symmetry, Enumerative Geometry, and Curve Counting: 27 Lines on a Cubic Surface." Meet the New Faculty in Claremont McKenna College Department of Mathematical Sciences Seminar. Monday, 2/12/2024. Same talk given in ANTC on March 6



"Presentations of Derived Categories." UC Irvine Seminar 2/1/2024. 


"Resolutions of the Diagonal and Fourier-Mukai Transforms." Claremont Consortium Colloquium. 9/27/2023


"A Positive Example for Modified King's Conjecture." Claremont Consortium Topology Seminar. 9/19/2023. 


"Planar conics." Graduate student seminar at Kansas State University. 3/28/2023. 


Beamer presentation from PhD dissertation defense. Kansas State University. March 9, 2023. 

"Log Differential Forms."  Junior Mirror Symmetry Seminar at Kansas State University. November 2022.


``Hilbert Polynomials." Graduate Student Seminar (GSS) at Kansas State University. 9/1/2022.


``What is: an Infinitesimal?" Differential Geometry Seminar at UIowa. March 2019.  A version of these notes was published in the AMS Graduate Student Blog  on August 28, 2019 at https://blogs.ams.org/mathgradblog/2019/08/28/32749/.

Title: Calculus with Schemes: Using the Dual Numbers to Understand Infinitesimals

Abstract: The dual numbers over the real line (R) offer a framework to understand algebraic constructions in undergraduate calculus by considering infinitesimal lengths to be nilpotent elements in the coordinate ring of the origin, considered as a subscheme of R. The main result here is that the dual numbers are isomorphic to the first infinitesimal neighborhood of the origin. Though this is not a new result, this construction invites questions of how to interpret additional scheme-theoretic infinitesimal neighborhoods of the origin, as well as infinitesimal deformations of varieties and schemes more generally. I will describe features of the dual numbers which suggest that there is an imaginary or non-real quality to infinitesimals over the real line. If time permits, I will also mention a connection to Lie algebras and tangent bundles. This talk references ResearchGate pre-print DOI: 10.13140/RG.2.2.17102.10563. 


``DG Categories and Homotopy Category of a DG Category" 7/9/18. Categories of Modules Mini-Course Lecture at Kansas State University. 


 ``Survey of Results in K-Theory", May 2018. Final presentation for Homological Algebra course at Kansas State University.


A Sketch of Mirror Symmetry as Batyrev Duality for Toric Varieties. Notes for a previous blog post. 2/13/2021