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KANSAS GRADUATE STUDENT CONFERENCE SCHEDULE
All talks are held in Snow 120 and are 30 minutes long.
Abstracts Can Be Found Below
Start Time
SPEAKER
Talk Title
10:30
SOPHIA RESTAD
So... What is Algebraic Geometry?
11:15
JIAYU ZHAO
Matrix Factorization
11:45
LUNCH
Soup, salad, and sandwiches provided in Snow 406.
1:30
DYLAN C. BECK
The Canonical Blow-Up of a Numerical Semigroup
2:15
RYAN FRIER
An Alternative Approach to Strichartz Inequality
3:00
MARK DENKER
Cut Complexes and Extending Fröberg's Theorem
SPEAKERS
Get to Know Them
SOPHIA RESTAD
So... What is Algebraic Geometry?
Algebraic geometry is a very broad subject that often seems impenetrable to outsiders. With this talk I will attempt to remedy that, giving a brief overview of what kind of spaces algebraic geometers like to think about.
JIAYU ZHAO
Matrix factorization
Matrix factorizations was first introduced by Eisenbud in the study of homological algebra of hyperplanes with possibly singularities. He showed that the minimal resolution of any module over the hyperplane will eventually becomes 2－periodic. States in modern language, this means that there is a triangulated equivalence between the homotopy category of matrix factorizations and the stable derived category of the hyperplane. In this talk I will briefly introduce his work and provide a few examples.
DYLAN C. BECK
The Canonical Blow-Up of a Numerical Semigroup
Recent work of Dao et al. illuminates the deep interplay between stable ideals, trace ideals, reflexive modules, and blow-up rings. Combining inspiration from these observations with new results obtained by Herzog, Stamate, et al. in the study of the canonical trace ideal of a numerical semigroup ring, we are naturally motivated to examine the blow-up of the canonical ideal in this setting. In joint work with Hailong Dao, we introduce two new classes of numerical semigroups -- divisive and Gorenstein canonical blow-up (GCB) numerical semigroups -- and give examples of both. Particularly, we prove that far-flung Gorenstein, divisive, and maximal embedding dimension three numerical semigroups are GCB.
RYAN FRIER
An Alternative Approach to Strichartz Inequality
In this paper, we study the extremal problem for the Strichartz inequality for the Schrödinger equation on R^2. We show that the solutions to the associated Euler-Lagrange equation are exponentially decaying in the Fourier space and thus can be extended to be complex analytic. Consequently we provide a new proof to the characterization of the extremal functions: the only extremals are Gaussian functions, which was investigated previously by Foschi and Hundertmark-Zharnitsky.
MARK DENKER
Cut Complexes and Extending Fröberg's Theorem
Fröberg's theorem and Stanley-Reisner theory lie in an interesting intersection of algebra, topology, and graph theory. In this talk we introduce cut complexes as a way of extending Fröberg's theorem and demonstrate interesting constructions, properties, and topologies of cut complexes.
