Previous talks

Spring 2023

Symmetrically Hyperbolic Polynomials

Kevin Shu

Groups, Extensions, and Cohomology

Akash Narayanan

The non-alcoholic dollar game drinking game

Danial Hwang

Fall 2022

Determinantal Representations and the Image of the Principal Minor Map

Abeer Al Ahmadieh

Idylls and Baker-Lorscheid Multiplicities

Trevor Gunn

Decidability in Number Theory

Ian Lewis

An Introductory Proof of the Compactness Theorem and Some Applications

Griffin Edwards

What is a matroid?

Tong Jin

What is a Coxeter group, and why is a Coxeter group?

Tong Jin

Sparse Quadratic Programs via Polynomial Roots

Kevin Shu

Polynomials over ordered blueprints and tracts

Trevor Gunn

Sparse Fourier sum-of-squares decomposition for nonnegative functions on abelian groups

Shengding Sun

Spring 2022

Log-concavity of coefficients of characteristic polynomials of matroids

Tong Jin (Georgia Tech)

Ranks of points via Macaulay 2 (2nd talk)

Jaewoo Jung (Georgia Tech)

Dual representation of polynomial modules with applications to partial differential equations

Marc Härkönen (Georgia Tech)

Ranks of points via Macaulay 2

Jaewoo Jung (Georgia Tech)

A computer program for matroid representation

Tianyi Zhang (Georgia Tech)

Hilbert's Tenth Problem and Generalizations

Ian Lewis (Georgia Tech)

Nonnegativity and Real-Rootedness

Kevin Shu (Georgia Tech)

Nonnegative symmetric polynomials and symmetric sums of squares at the limit

Jose Acevedo (Georgia Tech)

Tropical and algebraic divisors and projective embeddings

Trevor Gunn (Georgia Tech)

Braided Monoidal Categories and Fusion Categories

Akash Narayanan (Georgia Tech)

Hyperbolic generalization of linear algebra

Shengding Sun (Georgia Tech)

Finite automata and transfer matrices

Trevor Gunn (Georgia Tech)

Fall 2021

Apolarity for binary forms

Jaewoo Jung (Georgia Tech)

Introduction to Diophantine Approximation with Applications to Arithmetic Geometry

Ian Lewis (Georgia Tech)

Representation of Delta-matroids and the spinor varieties

Tong Jin (Georgia Tech)

Nonnegative Quadratics over Stanley Reisner Varieties

Kevin Shu (Georgia Tech)

Characterizing multigraded regularity on products of projective spaces

Mahrud Sayrafi (University of Minnesota)

Tropical intersection theory II

Trevor Gunn (Georgia Tech)

Tropical intersection theory I

Trevor Gunn (Georgia Tech)

The algebra of linear PDE

Marc Härkönen (Georgia Tech)

Spring 2021

Stable set polytopes in differential algebra

Rida Ait El Manssour (MPI-Leipzig)

The steady-state degree and mixed volume of a chemical reaction network

Cvetelina Hill (Georgia Tech)

Linear PDE with constant coefficients

Marc Härkönen (Georgia Tech)

Another interpretation of tropical rank.

Tianyi Zhang (Georgia Tech)

Comparison between SOS and PSD via an algebraic quantity

Jaewoo Jung (Georgia Tech)

A funny thing happened on the way to infinity: homotopy continuation on a compact toric variety

Timothy Duff (Georgia Tech)

Representations of Sl(2,C) in combinatorics

Trevor Gunn (Georgia Tech)

Fall 2020

Chain conditions in power series and polynomial rings

Hamed Mousavi (Georgia Tech)

Hankel index of a projected of rational curves

Jaewoo Jung (Georgia Tech)

Minimal problems and their monodromy groups

Timothy Duff (Georgia Tech)

Extreme Rays of Locally PSD Cones

Kevin Shu (Georgia Tech)

Introduction to Kajiwara-Payne Tropicalization II

Trevor Gunn (Georgia Tech)

Introduction to Kajiwara-Payne Tropicalization I

Trevor Gunn (Georgia Tech)

Noetherian operators and primary decomposition

Marc Härkönen (Georgia Tech)

Tropical convex hulls of polyhedral sets

Cvetelina Hill (Georgia Tech)

Linear algebra over tracts

Tianyi Zhang (Georgia Tech)

Hyperbolic polynomial and its application to locally PSD matrices

Shengding Sun (Georgia Tech)

Spring 2020

Computation of invariants and Hankel index on a variety of almost minimal degree

Jaewoo Jung (Georgia Tech) 

Hankel index of a projection of rational normal curve

Jaewoo Jung (Georgia Tech) 

Dual spaces and Noetherian operators

Marc Härkönen (Georgia Tech) 

Polynomials and multiplicities over hyperfields

Trevor Gunn (Georgia Tech) 

Fall 2019

Higher connectivity of the Bergman fan

Kisun Lee (Georgia Tech) 

Higher connectivity of the Bergman fan

Kisun Lee (Georgia Tech) 

Cayley-Bacharach Relations and Sums of Squares

Kevin Shu (Georgia Tech) 

Nonnegative symmetric polynomials and sums of squares with many variables (cont.)

Jose Acevedo (Georgia Tech) 

Nonnegative symmetric polynomials and sums of squares with many variables

Jose Acevedo (Georgia Tech) 

Tropical convex hulls of convex sets

Cvetelina Hill  (Georgia Tech) 

The foundation of a matroid

Tianyi Zhang  (Georgia Tech) 

The essential variety and degrees of minimal problems

Timothy Duff (Georgia Tech) 

The Jacobian Conjecture

Stephen McKean (Georgia Tech) 

Gram spectrahedra

Jaewoo Jung (Georgia Tech) 

Newton polygons and zeroes of polynomials

Trevor Gunn (Georgia Tech) 

Spring 2019

Rank of non-negative bivariate forms.

Jaewoo Jung (Georgia Tech) 

Graphical Models

Marc Härkönen (Georgia Tech) 

Milnor K-Theory

Stephen McKean (Georgia Tech) 

TBA

Justin Chen (Georgia Tech) 

Divisors on metric graphs and constructing tropicalizations of Mumford curves

Trevor Gunn (Georgia Tech) 

TBA 

Cvetelina Hill (Georgia Tech) 

Introduction to Intersection Theory

Tianyi Zhang (Georgia Tech) 

Introduction to Macaulay 2

Tim Duff (Georgia Tech) 

Fall 2018

TBA

Marcel Celaya (Georgia Tech)

The Clemens conjecture

Stephen McKean (Georgia Tech)

An Introduction to Étale Cohomology

Daniel Minahan (Georgia Tech)

The Littlewood-Richardson Rule

Trevor Gunn (Georgia Tech)

Symmetric functions and representations of the symmetric group

Trevor Gunn (Georgia Tech)

An Introduction to Spectral Sequences

Daniel Minahan (Georgia Tech)

Enriching Bézout’s Theorem

Stephen McKean (Georgia Tech)

Matroids and Grassmannians

Trevor Gunn (Georgia Tech)

An Introduction to Tropical Geometry

Trevor Gunn (Georgia Tech)

Some properties in Betti tables of Stanley-Reisner ideals

Jaewoo Jung (Georgia Tech)

Spring 2018

Graph Profiles via Sum of Squares

Jose Gabriel Acevedo Habeych (Georgia Tech)

Trace Test

Timothy Duff (Georgia Tech)

Bounds of the regularity of Stanley-Reisner ideals

Jaewoo Jung (Georgia Tech)

Some Corollaries about regularity of Stanley-Reisner ideals

Jaewoo Jung (Georgia Tech)

Methods for Certifying Solutions to Square Systems with D-finite Functions

Kisun Lee (Georgia Tech)

On Current Methods for Certifying System of Equations

Kisun Lee (Georgia Tech)

Matroids and log-concavity

Marcel Celaya (Georgia Tech)

Motives and motivic cohomology

Libby Taylor (Georgia Tech)

The Weyl Algebra

Marc Härkönen (Georgia Tech)

Introduction to differential operator rings

Marc Härkönen (Georgia Tech)

Automatic Sequences and Curves Over Finite Fields

Trevor Gunn (Georgia Tech)

Fall 2017

Kushnirenko's Theorem

Timothy Duff (Georgia Tech)

The relationship between Betti tables and clique sums on graphs II

Jaewoo Jung (Georgia Tech)

The relationship between Betti tables and clique sums on graphs

Jaewoo Jung (Georgia Tech)

Slack Matrices for Polytopes and Polyhedra

Kisun Lee (Georgia Tech)

Divisor Theory on Curves

Libby Taylor (Georgia Tech)