# Calendar

Oct
23
Wed
Logic seminar: Jack Yoon (II)
Oct 23 @ 2:30 pm – 3:30 pm
Applied Math Seminar: Nicolette Meshkat (Santa Clara University) @ Keller 402
Oct 23 @ 3:30 pm – 4:30 pm

Title: Structural Identifiability of Biological Models

Abstract: Parameter identifiability analysis addresses the problem of which unknown parameters of a model can be determined from given input/output data. If all of the parameters of a model can be determined from data, the parameters and the model are called identifiable. However, if some subset of the parameters can not be determined from data, the model is called unidentifiable. We examine this problem for the case of perfect input/output data, i.e. absent of any experimental noise. This is called the structural identifiability problem. We show that, even in the ideal case of perfect input/output data, many biological models are structurally unidentifiable, meaning some subset of the parameters can take on an infinite number of values, yet yield the same input/output data. In this case, one attempts to reparametrize the model in terms of new parameters that can be determined from data. In this talk, we discuss the problem of finding an identifiable reparametrization and give necessary and sufficient conditions for a certain class of linear compartmental models to have an identifiable reparametrization. We also discuss finding classes of identifiable models and finding identifiable submodels of identifiable models. Our work uses graph theory and tools from computational algebra. This is joint work with Elizabeth Gross and Anne Shiu.

Oct
29
Tue
Colloquium: Marissa Loving (Georgia Tech) @ Keller Hall 401
Oct 29 @ 4:00 pm – 5:00 pm

Title: Symmetries of Surfaces

Abstract: There are many ways to study surfaces: topologically, geometrically, dynamically, algebraically, and combinatorially, just to name a few. We will touch on some of the motivation for studying surfaces and their associated mapping class groups, which is the collection of symmetries of a surface. We will also describe a few of the ways that these different perspectives for studying surfaces come together in beautiful and sometimes unexpected ways.

Oct
30
Wed
Logic seminar: Kameryn Williams
Oct 30 @ 2:30 pm – 3:30 pm

I will speak about the recent paper “Condensable models of set theory” by Ali Enayat. The abstract can be found here: https://arxiv.org/abs/1910.04029

Nov
6
Wed
PhD defense for Don Krasky @ Keller 401
Nov 6 @ 3:00 pm – 5:00 pm
Nov
13
Wed
Logic seminar: Sam Birns
Nov 13 @ 2:30 pm – 3:30 pm
Nov
20
Wed
Logic seminar: Sam Birns
Nov 20 @ 2:30 pm – 3:30 pm
Nov
27
Wed
Colloquium: Elijah Liflyand (Bar-Ilan University) @ Keller 401
Nov 27 @ 3:30 pm – 4:30 pm

Speaker: Elijah Liflyand (Bar-Ilan University)
Title: A tale of two Hardy spaces

Abstract:
New relations between the Fourier transform of a function of bounded
variation and the Hilbert transform of its derivative are revealed.
If we do not distinguish between the cosine and sine transforms and consider
the general Fourier transform of $f$, direct calculations give the belonging
of the derivative $f’$ to the real Hardy space $H^1$ as a sufficient condition
for the integrability of the Fourier transform. Our analysis is more delicate.
The main result is an asymptotic formula for the {bf cosine} Fourier
transform, while much earlier known results gives an asymptotic formula
for the sine Fourier transform. The difference is achieved by assuming that
the derivative belongs to different subspaces of $H^1$. However, this tale of
each of the two subspaces were impossible if we would not have a new proof
even for the old result. The known proofs used to give strong priority just to
the sine transform. Interrelations of various function spaces are studied
in this context, first of all of these two types of Hardy spaces. The obtained
results are used for proving completely new results on the integrability
of trigonometric series.