Mathematics Program Presents
Student Talks in Mathematics
Tuesday, November 16, 2021
Hegeman 102
4:00 pm – 5:00 pm EST/GMT-5
Tina Giorgadze4:00 pm – 5:00 pm EST/GMT-5
"Building an Agent-based Computational Model of Chimeric Antigen Receptor (CAR) T-Cell Immunotherapy in Triple-Negative Breast Cancer Using Binary Distribution of Antigens"
Hannah Kaufmann
"Minimal Presentation Sizes of Numerical Semigroups"
A numerical semigroup is a subset of integers closed under addition, while a minimal presentation is a choice of minimal relations between generators of the numerical semigroup. It is a well-known fact that if m is the smallest positive element, then the size of the minimal presentation is at most m choose 2. Finding the possible minimal presentation sizes of numerical semigroups whose smallest positive element, or multiplicity, is m has been a long-standing open problem. In this talk, we introduce the role of embedding dimension in determining the attainable minimal presentation sizes. For each pairing of multiplicity and embedding dimension, we present multiple classes of numerical semigroups and pose upper and lower bounds. Our methods are not only combinatorial, but also involve posets and betti elements.
Verity Scheel
"Embedding Dimensions of Simplicial Complexes on Few Vertices"
As the result of summer research with Steve Simon (Bard) and Florian Frick (CMU), we found a straightforward characterization of simplicial complexes on few vertices that embed into the d-sphere. Simplicial complexes can be studied both as geometric objects embedded into space and as combinatorial set systems, and our result provides a simple combinatorial property that corresponds to topological characteristics of the same object. In particular, a simplicial complex on d+3 vertices embeds into the d-sphere if and only if its non-faces do not form an intersecting family. Like the case of planar graphs, we show in addition that such complexes satisfy the rigidity property that continuous and linear embeddability are equivalent.
For more information, call 845-758-7191, or e-mail [email protected].
Time: 4:00 pm – 5:00 pm EST/GMT-5
Location: Hegeman 102