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## Analysis Learning Seminar

- 9/6
*Analysis Learning Seminar*

Faculty Research Showcase, Part I

UConn Math Faculty#### Analysis Learning Seminar

Friday, September 6th, 2019

Faculty Research Showcase, Part I

UConn Math Faculty

3:30 PM - 4:30 PM

Storrs Campus

Monteith 214We will kick off the Fall 2019 semester with short talks by members of the math faculty, introducing their areas of research. Talks are intended to be accessible to all graduate students and faculty in the math department, including the first year graduate students. Everyone is welcome to attend.

Confirmed Speakers:

Masha Gordina

Sasha Teplayev

Ling Xiao

Contact Information: Matthew Badger (matthew.badger@uconn.edu) More - 9/13
*Analysis Learning Seminar*

Faculty Research Showcase, Part II

UConn Math Faculty#### Analysis Learning Seminar

Friday, September 13th, 2019

Faculty Research Showcase, Part II

UConn Math Faculty

3:30 PM - 4:30 PM

Storrs Campus

Monteith 204This week we will hear three more short talks by faculty members describing their research interests. All members of the department are welcome, especially first and second year graduate students.

Confirmed Speakers:

Iddo Ben-Ari

Dmitriy Leykekhman

Ambar Sengupta

Contact Information: Matthew Badger (matthew.badger@uconn.edu) More - 9/20
*Analysis Learning Seminar*

Brownian Motion and Ito's Integral

Marco Carfagnini (UConn)#### Analysis Learning Seminar

Friday, September 20th, 2019

Brownian Motion and Ito's Integral

Marco Carfagnini (UConn)

3:30 PM - 4:30 PM

Storrs Campus

Monteith 214This talk is a short review of basic stochastic calculus. We will define a stochastic process first, and then focus on the (real-valued) Brownian motion and its properties (independence of the increments, regularity of paths etc). Afterwards, we will define the Ito's integral and state Ito's Lemma. In particular, we will see why analytic construction (such as Riemann-Stieltjes integral) can not be applied to define the integral of a function against the Brownian motion.

No graduate probability course is needed as prerequisite.

Contact Information: Matthew Badger (matthew.badger@uconn.edu) More - 9/27
*Analysis Learning Seminar*

Laplacians and Spectra on Laakso Spaces

Benjamin Steinhurst (McDaniel College)#### Analysis Learning Seminar

Friday, September 27th, 2019

Laplacians and Spectra on Laakso Spaces

Benjamin Steinhurst (McDaniel College)

3:30 PM - 4:30 PM

Storrs Campus

Monteith 214Laakso spaces are a family of fractal spaces that are constructed from a sequence of approximations via a projective (inverse) limit. This gives rise to a direct limit of the associated function spaces, ($$L^{2}$$, $$Dom(\Delta)$$, $$\ldots$$). The virtue of this is that the Laplacian is very well understood and has an explicitly computable spectrum and eigenspaces. We construct all of these objects and discuss how the spectrum changes in response to small changes in the geometry of the fractal.

Contact Information: Matthew Badger (matthew.badger@uconn.edu) More - 10/4
*Analysis Learning Seminar*

Monsters versus the Dream Universe: the Axiom of Choice in Analysis

Nathaniel Eldredge (University of Northern Colorado)#### Analysis Learning Seminar

Friday, October 4th, 2019

Monsters versus the Dream Universe: the Axiom of Choice in Analysis

Nathaniel Eldredge (University of Northern Colorado)

3:30 PM - 4:30 PM

Storrs Campus

Monteith 214The axiom of choice is widely accepted in mathematics, but in analysis, it lets you construct a number of "monsters": non-measurable sets, discontinuous linear functionals, paradoxical hat guessing strategies, and so on. In this talk, we'll look at some alternative axioms that result in a "dream universe" where these monsters don't exist, though perhaps a few other things are a little different. Along the way, we'll see some interesting tidbits from the foundations of mathematics, and start to get a sense for "how much choice" is used in various parts of analysis.

Contact Information: Matthew Badger (matthew.badger@uconn.edu) More - 10/11
*Analysis Learning Seminar*

Introduction to Rough Path Theory

Guang Yang (UConn)#### Analysis Learning Seminar

Friday, October 11th, 2019

Introduction to Rough Path Theory

Guang Yang (UConn)

3:30 PM - 4:30 PM

Storrs Campus

Monteith 214The theory of rough path can be briefly described as a non-linear extension of the classical theory of controlled differential equations which is robust enough to allow a deterministic treatment of stochastic differential equations, or even differential equations driven by much rougher signals than semi-martingales. In this talk, I will present the most fundamental ideas of the theory and discuss some examples.

Contact Information: Matthew Badger (matthew.badger@uconn.edu) More - 10/18
*Analysis Learning Seminar*

Holonomy of Riemannian Manifolds and Berger's Classification

Gianmarco Molino (UConn)#### Analysis Learning Seminar

Friday, October 18th, 2019

Holonomy of Riemannian Manifolds and Berger's Classification

Gianmarco Molino (UConn)

3:30 PM - 4:30 PM

Storrs Campus

Monteith 214Equipping a Riemannian manifold with an affine connection allows for a notion of parallel transport of vector fields. Considering loops based at a fixed point, the parallel transport induces a subgroup of the orthogonal transformations of the tangent space of vector fields known as the holonomy group of the manifold. The list of possible holonomy groups (classified by Cartan and Berger) is remarkably short, and there is a strong relationship between the holonomy group of a manifold and its global geometry, which we will explore in this talk.

Contact Information: Matthew Badger, matthew.badger@uconn.edu More - 10/25
*Analysis Learning Seminar*

d-bar Neumann problems and geometric applications in several complex variables

Gunhee Cho (UConn)#### Analysis Learning Seminar

Friday, October 25th, 2019

d-bar Neumann problems and geometric applications in several complex variables

Gunhee Cho (UConn)

3:30 PM - 4:30 PM

Storrs Campus

Monteith 214We will introduce d-bar Neumann operator and subelliptic estimates on pseudoconvex domains in $$\mathbb{C}^n$$ and we will try to see geometric applications that are very closely related to complex geometry, sub-Riemannian geometry, and CR-geometry and algebraic geometry.

Contact Information: Matthew Badger (matthew.badger@uconn.edu) More - 11/1
*Analysis Learning Seminar*

Bartnik Boundary Conditions in General Relativity I

Zhongshan An (UConn)#### Analysis Learning Seminar

Friday, November 1st, 2019

Bartnik Boundary Conditions in General Relativity I

Zhongshan An (UConn)

3:30 PM - 4:30 PM

Storrs Campus

Monteith 214The Bartnik boundary conditions are very well-known in general relativity. They play a key role when measuring the quasi-local mass of a bounded manifold with boundary. When the spacetime is static, Bartnik boundary conditions consists of the induced metric g and the mean curvature H on the boundary of the manifold. This pair (g,H) of boundary data is much studied by mathematicians, as they are closely related to not only Bartnik mass, but also various notions of quasi-local mass such as the Brown-York mass and the Hawking mass.

In general relativity, the existence of extensions of Bartnik boundary data which are Einstein manifolds is a very interesting and open problem. A fundamental question to approach this problem is whether the Bartnik boundary conditions are elliptic for the static/stationary vacuum spacetime.

In this mini course, I will start with an introduction to the ADM mass and the quasi-local mass in the first lecture. The second lecture will be devoted to discussions of Bartnik boundary data in the static spacetime, including the ellipticity and a local existence result. In the last lecture we will generalize these results from static to stationary spacetime.

Contact Information: Matthew Badger (matthew.badger@uconn.edu) More - 11/15
*Analysis Learning Seminar*

Bartnik Boundary Conditions in General Relativity II

Zhongshan An (UConn)#### Analysis Learning Seminar

Friday, November 15th, 2019

Bartnik Boundary Conditions in General Relativity II

Zhongshan An (UConn)

3:30 PM - 4:30 PM

Storrs Campus

Monteith 214The Bartnik boundary conditions are very well-known in general relativity. They play a key role when measuring the quasi-local mass of a bounded manifold with boundary. When the spacetime is static, Bartnik boundary conditions consists of the induced metric g and the mean curvature H on the boundary of the manifold. This pair (g,H) of boundary data is much studied by mathematicians, as they are closely related to not only Bartnik mass, but also various notions of quasi-local mass such as the Brown-York mass and the Hawking mass.

In general relativity, the existence of extensions of Bartnik boundary data which are Einstein manifolds is a very interesting and open problem. A fundamental question to approach this problem is whether the Bartnik boundary conditions are elliptic for the static/stationary vacuum spacetime.

In this mini course, I will start with an introduction to the ADM mass and the quasi-local mass in the first lecture. The second lecture will be devoted to discussions of Bartnik boundary data in the static spacetime, including the ellipticity and a local existence result. In the last lecture we will generalize these results from static to stationary spacetime.

Contact Information: Matthew Badger (matthew.badger@uconn.edu) More - 12/6
*Analysis Learning Seminar*

Bartnik Boundary Conditions in General Relativity III

Zhongshan An (UConn)#### Analysis Learning Seminar

Friday, December 6th, 2019

Bartnik Boundary Conditions in General Relativity III

Zhongshan An (UConn)

3:30 PM - 4:30 PM

Storrs Campus

Monteith 214The Bartnik boundary conditions are very well-known in general relativity. They play a key role when measuring the quasi-local mass of a bounded manifold with boundary. When the spacetime is static, Bartnik boundary conditions consists of the induced metric g and the mean curvature H on the boundary of the manifold. This pair (g,H) of boundary data is much studied by mathematicians, as they are closely related to not only Bartnik mass, but also various notions of quasi-local mass such as the Brown-York mass and the Hawking mass.

In general relativity, the existence of extensions of Bartnik boundary data which are Einstein manifolds is a very interesting and open problem. A fundamental question to approach this problem is whether the Bartnik boundary conditions are elliptic for the static/stationary vacuum spacetime.

In this mini course, I will start with an introduction to the ADM mass and the quasi-local mass in the first lecture. The second lecture will be devoted to discussions of Bartnik boundary data in the static spacetime, including the ellipticity and a local existence result. In the last lecture we will generalize these results from static to stationary spacetime.

Contact Information: Matthew Badger (matthew.badger@uconn.edu) More

*Past talks in or after Spring 2019 are accessible through the UConn Events Calendar.*

List of talks prior to Spring 2019.

List of talks prior to Spring 2019.