Binghamton University Graduate Conference in Algebra and Topology

## November 2-3, 2019

Graduate students of all levels and faculty are invited to register to give a 30 minute talk. Talks may be expository or on current research.

Abstract submission is now closed. If you would like to submit a talk, please use our Title and Abstract Submission Form. The deadline for submitting a talk is October 21st.

Funding requests are now closed. To request funding, please use our Funding Request Form. The deadline for requesting funding is October 2nd.

## Keynote Speakers

Marcelo Aguiar Cornell University
Mobius functions for real hyperplane arrangements We discuss a number of algebraic structures attached to a real hyperplane arrangement, leading to the beginnings of a theory of noncommutative Mobius functions. Background on hyperplane arrangement and Mobius functions will be reviewed. The talk will contain geometric, combinatorial and algebraic aspects and there will be many pictures. All based on joint work with Swapneel Mahajan.
Jonathan Barmak La Universidad de Buenos Aires
Homotopy invariants and the fixed point property A space has the fixed point property (FPP) if every self map has a fixed point. We know that disks and, in general, compact polyhedra with trivial rational homology have the FPP. On the other hand, polyhedra with non-trivial rational $$H_1$$ do not have the FPP. The connection between the FPP and homology/homotopy groups is very weak when we consider more general (non-Hausdorff) spaces. We will see that given any compact CW-complex X there is a (finite!) topological space with the FPP having the same homotopy invariants as X.
Matthias Beck San Francisco State University
Quasipolynomials in Discrete Geometry and Combinatorial Commutative Algebra A quasipolynomial is a function of the form $$q(t) = c_d(t) t^d + … + c_1(t) t + c_0(t)$$ where $$c_0(t), c_1(t), …, c_d(t)$$ are periodic functions. The least common period of $$c_0(t), c_1(t), …, c_d(t)$$ is the period of $$q(t)$$, and together with the degree $$d$$ it gives us an idea about the (computational) complexity of $$q(t)$$. Quasipolynomials occur frequently as counting functions in combinatorial commutative algebra (as Hilbert functions of monomial algebras) and discrete geometry (as Ehrhart functions of rational polytopes). Using joint work with Maryam Farahmand on antimagic graph counting functions as a guiding example, we present an ansatz to computing quasipolynomials that makes use of techniques from both commutative algebra and discrete geometry.