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Series: Analysis Seminar

In this talk I will introduce a Tb Theorem that characterizes all Calderón-Zygmund operators that extend compactly on L^p(R^n) by means of testing functions as general
as possible.
In the classical theory for boundedness, the testing functions satisfy a non-degeneracy property called accretivity, which essentially implies the existence of a positive lower bound
for the absolute value of the averages of the testing functions over all dyadic cubes. However, in the setting of compact operators, due to their better properties, the hypothesis of accretivity can be relaxed to a large extend.
As a by-product, the results also describe those Calderón-Zygmund operators whose boundedness can be checked with non-accretive testing functions.

Series: Research Horizons Seminar

Series: PDE Seminar

Almost all biological activities involve transport and distribution of ions and charged particles. The complicated coupling and competition between different ionic solutions in various biological environments give the intricate specificity and selectivity in these systems. In this talk, I will introduce several extended general diffusion systems motivated by the study of ion channels and ionic solutions in biological cells. In particular, I will focus on the interactions between different species, the boundary effects and in many cases, the thermal effects.

Series: Math Physics Seminar

Series: Math Physics Seminar

Existence of ballistic transport for Schr ̈odinger operator with a quasi-
periodic potential in dimension two is discussed. Considerations are based on the
following properties of the operator: the spectrum of the operator contains a semiaxis
of absolutely continuous spectrum and there are generalized eigenfunctions being close
to plane waves ei⟨⃗k,⃗x⟩ (as |⃗k| → ∞) at every point of this semiaxis. The isoenergetic
curves in the space of momenta ⃗k corresponding to these eigenfunctions have a form
of slightly distorted circles with holes (Cantor type structure).

Series: Algebra Seminar

In this talk we will discuss the following question: When does there exist a curve of degree d and genus g passing through
n general points in P^r? We will focus primarily on what is known in the case of space curves (r=3).

Series: Geometry Topology Seminar

Peter Lambert-Cole: Mutant knots are notoriously hard to distinguish. Many, but not all, knot invariants take the same value on mutant pairs. Khovanov homology with coefficients in Z/2Z is known to be mutation-invariant, while the bigraded knot Floer homology groups can distinguish mutants such as the famous Kinoshita-Terasaka and Conway pair. However, Baldwin and Levine conjectured that delta-graded knot Floer homology, a singly-graded reduction of the full invariant, is preserved by mutation. In this talk, I will give a new proof that Khovanov homology mod 2 is mutation-invariant. The same strategy can be applied to delta-graded knot Floer homology and proves the Baldwin-Levine conjecture for mutations on a large class of tangles. -----------------------------------------------------------------------------------------------------------------------------------------------Alex Zupan: Generally speaking, given a type of manifold decomposition, a natural
problem is to determine the structure of all decompositions for a fixed
manifold. In particular, it is interesting to understand the space of
decompositions for the simplest objects. For example, Waldhausen's
Theorem asserts that up to isotopy, the 3-sphere has a unique Heegaard
splitting in every genus, and Otal proved an analogous result for
classical bridge splittings of the unknot. In both cases, we say that
these decompositions are "standard," since they can be viewed as generic
modifications of a minimal splitting. In this talk, we examine a
similar question in dimension four, proving that -- unlike the situation
in dimension three -- the unknotted 2-sphere in the 4-sphere admits a
non-standard bridge trisection. This is joint work with Jeffrey Meier.

Monday, November 6, 2017 - 13:55 ,
Location: Skiles 005 ,
Prof. Kevin Lin ,
University of Arizona ,
klin@math.arizona.edu ,
Organizer: Molei Tao

Weighted direct samplers, sometimes also called importance
samplers, are Monte Carlo algorithms for generating
independent, weighted samples from a given target
probability distribution. They are used in, e.g., data
assimilation, state estimation for dynamical systems, and
computational statistical mechanics. One challenge in
designing weighted samplers is to ensure the variance of the
weights, and that of the resulting estimator, are
well-behaved. Recently, Chorin, Tu, Morzfeld, and coworkers
have introduced a class of novel weighted samplers called
implicit samplers, which possess a number of nice empirical
properties. In this talk, I will summarize an asymptotic
analysis of implicit samplers in the small-noise limit and
describe a simple method to obtain a higher-order accuracy.
I will also discuss extensions to stochastic differential
equatons. This is joint work with Jonathan Goodman, Andrew
Leach, and Matthias Morzfeld.

Series: CDSNS Colloquium

We present a mean field model of electroencephalographic activity in the brain, which is composed of a system of coupled ODEs and PDEs. We show the existence and uniqueness of weak and strong solutions of this model and investigate the regularity of the solutions. We establish biophysically plausible semidynamical system frameworks and show that the semigroups of weak and strong solution operators possess bounded absorbing sets. We show that there exist parameter values for which the semidynamical systems do not possess a global attractor due to the lack of the compactness property. In this case, the internal dynamics of the ODE components of the solutions can create asymptotic spatial discontinuities in the solutions, regardless of the smoothness of the initial values and forcing terms.

Series: AMS Club Seminar

All of us have seen talks where the speaker uses slides. Some are great,
and some are awful. Come and learn how to make great slide decks and
how to avoid making awful ones. We will share a number of pieces of
software that are easy to use and that can help
you to improve your slide decks. We will also discuss best practices
and dissect several short slide decks together. Next week there will be a follow-up, hands-on workshop on using the software Inkscape to create mathematical
figures for talks, posters, and papers.