Colloquium

Irrationality measure functions

01/31/2018 - 4:15pm
01/31/2018 - 5:15pm
Speaker: 
Nikolay Moshchevitin
Abstract: 

We will discuss various problems dealing with approximation of real numbers by rationals.Let $\alpha$ be a real number. A rational fraction  $p/q$ is defined to be a best approximation to $\alpha$ if $ |\alpha q'-p'|> |\alpha q -p|$ for all fractions $p'/q'$ with $ q'<q$. The sequence of the best approximations to $\alpha$  determine the irrationality measure function $\psi_\alpha (t)$ which has nice properties. 

Where: 
Freeberg Forum, LC 62, Kravis Center, CMC

An introduction to image processing, its applications, and the problem of imaging through optical turbulence

11/29/2017 - 4:15pm
11/29/2017 - 5:15pm
Speaker: 
Mario Micheli (HMC)
Abstract: 

In this talk I will give an overview of the exciting and growing field of image processing, by introducing how images and video can be modeled and manipulated mathematically. I will provide examples of the typical problems that are studied in this discipline, and present an array of applications in medicine, astronomy, atmospheric science, security, navigation systems, and others in data science and information technology. Also, I shall present the research problem of image reconstruction under "optical turbulence", i.e. the optical phenomenon caused by light rays being refracted to form distorted images at the observer's location: this typically occurs when looking at objects at a distance in hot climates, or underwater in the presence of temperature gradients (i.e., when the water temperature is not the same at different locations). The results of an imaging recovery algorithm will also be illustrated.

Where: 
Argue Auditorium, Millikan, Pomona College

In No Hurry to Deviate : Extensions of Bernstein's Lethargy Theorem

02/21/2018 - 4:15pm
02/21/2018 - 5:15pm
Speaker: 
Asuman Aksoy (CMC)
Abstract: 

The formal beginnings of approximation theory date back to 1885, with Weierstrass' celebrated approximation theorem. The discovery that every continuous function defined on a closed interval $[a,b]$ can be uniformly approximated as closely as desired by a polynomial function immediately prompted many new questions. One such question concerned approximating functions with polynomials of limited degree. That is, if we limit ourselves to polynomials of degree at most $n$, what can be said of the best approximation? As it turns out, there is no unified answer to this question. In fact, S. N. Bernstein (1938) showed that there exists functions whose best approximation converges arbitrarily slowly as the degree of the polynomial rises. In this talk, we take this aptly-named ``Lethargy theorem" of Bernstein and present two extensions. We'll show one of these extensions shrinks the interval for best approximation by half while the other gives a surprising equivalence to reflexivity in Banach spaces. Put colloquially, this shows that if you are in no hurry to deviate, you might reach a nice spot!

(Joint work with Q. Peng and G. Lewicki).

Where: 
Freeberg Forum, LC 62, Kravis Center, CMC

Exploiting Symmetries in Computations with Lattice Polytopes

12/06/2017 - 4:15pm
12/06/2017 - 5:15pm
Speaker: 
Achill Schürmann(University of Rostock)
Abstract: 
Exploiting symmetry in integer linear programming and lattice
point counting are two difficult problems for which no good general
approach exists. In fact, standard techniques work particularly poor
on symmetric problems. In this talk we give an overview about ongoing
work on new symmetry exploiting techniques for these two fundamental 
problem classes involving lattice polytopes. We in particular present 
some new ideas of decomposing lattice polytopes and give some initial 
proof-of-concept results applying these new techniques.
Where: 
Argue Auditorium, Millikan, Pomona College

Bingo Paradoxes

11/15/2017 - 4:15pm
11/15/2017 - 5:15pm
Speaker: 
Art Benjamin (HMC)
Abstract: 

Imagine you are walking past a crowded Bingo parlor with hundreds of people playing. Suddenly you hear one person excitedly call out "Bingo!". Is it more likely that they have 5 in a row or 5 in a column (or are they the same)? Or is the most probable outcome diagonal? The answers may surprise you.
This is joint work with HMC alums Joseph Kisenwether and Ben Weiss, and Pomona alum Jay Cordes.

Where: 
Argue Auditorium, Millikan, Pomona College

Sewing Riemannian Manifolds with Positive Scalar Curvature

10/04/2017 - 4:15pm
10/04/2017 - 5:15pm
Speaker: 
Jorge Basilio(Pitzer)
Abstract: 
We explore to what extent one may hope to preserve geometric properties of three dimensional manifolds with lower scalar curvature bounds under Gromov-Hausdorff and Intrinsic Flat limits. We introduce a new construction, called sewing, of three dimensional manifolds that preserves positive scalar curvature. We then use sewing to produce sequences of such manifolds which converge to spaces that fail to have nonnegative scalar curvature in a certain generalized sense. These examples demonstrate that a certain question of Gromov is false. 

Where: 
Argue Auditorium, Millikan, Pomona College

Prime numbers and their biases

09/20/2017 - 4:15pm
09/20/2017 - 5:15pm
Speaker: 
Stephan Garcia ( Pomona College )
Abstract: 

We survey some classical and modern results about prime numbers.  In particular, we highlight some remarkable biases displayed by prime pairs that were discovered by Pomona undergraduates in 2017.


Where: 
Argue Auditorium, Millikan, Pomona College

Pre-colloquium party

08/30/2017 - 4:15pm
08/30/2017 - 6:00pm
Speaker: 
TBA
Abstract: 

TBA

Where: 
CGU Math South

Stochastic calculus of stem cells

09/27/2017 - 4:15pm
09/27/2017 - 5:15pm
Speaker: 
Natalia Komarova (UCI)
Abstract: 
Stem cells are an important component of tissue architecture. Identifying the exact regulatory circuits that can stably maintain tissue homeostasis (that is, approximately constant size) is critical for our basic understanding of multicellular organisms. It is equally critical for figuring out how tumors circumvent this regulation, thus providing targets for treatment. Despite great strides in the understanding of the molecular components of stem-cell regulation, the overall mechanisms orchestrating tissue homeostasis are still far from being understood. Typically, tissue contains the stem cells, transit amplifying cells, and terminally differentiated cells. Each of these cell types can potentially secrete regulatory factors and/or respond to factors secreted by other types. The feedback can be positive or negative in nature. This gives rise to a bewildering array of possible mechanisms that drive tissue regulation. In this talk I describe a novel stochastic method of studying stem cell lineage regulation, which is based on population dynamics and ecological approaches. The method allows to identify possible numbers, types, and directions of control loops that are compatible with stability, keep the variance low, and possess a certain degree of robustness. I will also discuss evolutionary optimization and cancer-delaying role of stem cells.
 
 
 
Where: 
Argue Auditorium, Millikan, Pomona College

Reactive Processes in Random Media

09/06/2017 - 4:15pm
09/06/2017 - 5:15pm
Speaker: 
Andrej Zlatos (UCSD)
Abstract: 

We study propagation of reactive processes, such as forest fires or spreading of invasive species, in random heterogeneous environments and show that homogenization takes place under suitable hypotheses.  That is, on large space-time scales the effects of the small-scale heterogeneities average out, and the dynamics of solutions to the partial differential equations (PDEs) that model these processes become effectively homogeneous.  Interestingly, while the original PDEs are second-order (reaction-diffusion) equations, the "homogenized" PDEs that govern the large-scale dynamics are first-order (Hamilton-Jacobi) equations.  A key ingredient in this work is a new relationship between spreading speeds and front speeds for these models, as well as a new method to prove existence of these speeds.  

Where: 
Argue Auditorium, Millikan, Pomona College
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