**Time & Place:**Thursday 11 am, Thackeray 703

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**Schedule of Talks**

**September 20***Speaker*: Tracy Stepien*Title*: Parameter Sensitivities and Modeling of the Aortic Valve*Abstract*: In this talk, I will discuss two projects I worked on this past summer at workshops hosted by the Mathematical Biosciences Institute. The first part of the talk will be on parameter sensitivities and continuous Markov chains. We analytically and numerically compare three methods for determining parameter sensitivities for chemical reaction networks. The second part of the talk will be on developing a mathematical model for microindentation of aortic valve leaflets to aid in the determination of local micromechanical properties. I will also discuss how, when, and why to apply for summer workshops.**October 11***Speaker*: Cheng Yu*Title*: The global solutions to incompressible Navier-Stokes-Vlasov equations*Abstract*: The system of particles coupled with fluid is discussed in this talk. The particles are described by a Vlasov equation, and the fluid is governed by the forced incompressible Navier-Stokes equations. The interaction with fluid phase governed by Navier-Stokes equations is taken into account through a source term. In this talk, we will discuss the existence and uniqueness to such a resulting system, namely Navier-Stokes-Vlasov equations.**October 25***Speaker*: Jonathan Holland*Title*: Microtwistors*Abstract*: The dual of the Euclidean plane is the space of lines in it. Associated to a smooth curve in the plane is the dual curve, consisting of the locus of tangent lines to the original curve. This duality between a curve and its dual has important applications to many areas of applied mathematics: mechanics, nonlinear optics, second order differential equations, and scalar conservation laws. In fact, the duality is essentially the lowest-dimensional case of "twistor theory", a geometric machinery that associates data between two geometrical spaces that are mutually dual. This talk surveys some of the various disguises that such "microtwistors" take, including the inviscid Burgers' equation (and its inhomogeneous version), the Crofton formula, and duality of second order ordinary differential equations. Although twistor theory is generally thought of as a theory of complex variables, the talk will emphasize the real variable aspects. A major theme is that there are legitimate and deep questions in low dimensions that involve only real variables. For example, under the duality between plane curves and dual curves, a smooth curve can go to a non-smooth curve. So the appropriate language to discuss this duality appropriately is not differential calculus, but rather is geometric measure theory, and we are led immediately to consider deep theorems of Besicovitch and Federer. This duality can also be extended to curves on Riemann surfaces, but then noncommutative geometry appears as the natural arena to realize this duality.**November 8***Speaker*: Torrey Gallagher*Title*: An introduction to divergent series*Abstract*: The study of divergent series began in the 18th century as mathematicians attempted to rigorously define convergence for infinite sums. We give an overview of methods for calculating divergent series, focusing on the work done by Abel, Euler, Cesaro, and Borel. This addresses not only the justifications and uses of assigning values to divergent sums, but also the at times absurd and unintuitive nature of a calculus that allows us to responsibly assert that 1+2+3+4+... = -1/12.**November 29***Speaker*: Merve Kovan-Bakan*Title*: Comparable and Incomparable Continua*Abstract*: Two continua are comparable if there is a continuous map onto from one to the other. In this talk, we will see an uncountable family of incomparable continua, which look like wedding cakes. We will also look into the following question: is there a continuum which is comparable with all continua?**December 13***Speaker*: Jared Burns*Title*: M-Calculi: Multiplying and Means*Abstract*: The Riemann Integral we know and love is based on arithmetic averages. Therefore, a natural question is the following: What happens if we change the average to another type.say a geometric average. In this, we venture into the research of Vito Volterra among others, and define a collection of what we will call M-Calculi and m-integrals (some of which are what are often referred to as Non-Newtonian Calculi). We will discuss the relationship between the usual Calculus and some of the M-Calculi. In particular, we learn that m-integrals are multiplicative, and we will have a derivative (denoted with a star *) such that (f/g)* = f*/g*.