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Katherine Funk | Katherine Funk | EWG336 | Title: Discrete Maturity-Structured Model of Cell Differentiation with Applications to Acute Myelogenous Leukemia <br><br> Abstract: Hematopoiesis is the formation of cellular blood components. In acute myeloid leukemia, this process is disrupted by a blocking of cell differentiation. We will develop a compartment model to describe the normal process of hematopoiesis considering multiple generations of immature and mature cells. We will discuss conditions that give us both trivial and nontrivial steady state values as well as note the stability of each kind of steady state that may arise. We use numerical simulations to show how differentiation constants can affect the steady states and how the cell densities change when we block cell differentiation for one generation. This is an expository talk. | 12/4/2019 4:15:00 PM | 12/4/2019 5:15:00 PM | False | |

Teddy Mishura | Teddy Mishura | EWG336 | Title: Limits of Dense Graph Sequences <br><br> Abstract: In this talk we will explore the idea of so-called "convergent graph sequences", which are sequences of graphs {G_n} said to converge to some limiting object. One can describe such an object in terms of graphons, symmetric, measurable functions from [0,1]^2 to [0,1] that can be used to generalize finite graphs. This leads to an interesting intersection between analysis and graph theory, where techniques from one field can be used to solve problems from the other. The basic theory of graphons is built and an equivalence is shown between the existence of a convergent graph sequence and the existence of its limiting graphon. We note also that it is required that the edges in the graphs in such a sequence be dense (i.e. of order |V(G_n)|^2) or the sequence will converge to the zero graphon. This will be an expository talk. | 11/20/2019 4:15:00 PM | 11/20/2019 5:15:00 PM | False | |

Himanshu Gupta | Himanshu Gupta | EWG336 | Title: Equiangular Lines in Euclidean Space<br><br> Abstract: A set of lines in R^d such that the angle between any two distinct lines is the same is called a set of equiangular lines. A well known and natural problem is to determine N(d), the maximum possible cardinality of a set of equiangular lines in R^d. The problem of determining N(d) is one of the founding problems of algebraic graph theory, despite the fact that at first sight it has little connection to graphs. In this talk we will see the connections of this problem with graph theory and compute an upper bound on N(d). This will be an expository talk. | 11/13/2019 4:15:00 PM | 11/13/2019 5:15:00 PM | False | |

Benjamin Nassau | Benjamin Nassau | EWG336 | Title: Summer's Cool: the Mathematical Sciences Research Institute <br><br> Abstract: Come find out one of the many ways to spend a summer as a mathematician! We'll detail what MSRI is and talk about the polynomial method, a cutting-edge technique making phenomenal advances in many areas of math. | 10/30/2019 3:15:00 PM | 10/30/2019 4:15:00 PM | False |

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