alorent
 
Search this site

UC Analysis Seminar

Winter Quarter 2010. (Usually) Friday at 1pm. Old Chem 807. 

15th Jan. Leonid Slavin. Old Chem 602

 'Bellman functions for the dyadic maximal operator. Part 2'

22th Jan. Jun-Feng Li. University of Alabama. At 12pm. Old Chem 807

 ' Isoperimetric quermassintegral inequalities and fully nonlinear geometric PDE '

Abstract: In this talk, we are interested in proving the quermassintegral inequalitites which are originated from convex geometry and can be viewed as a generalization to the classical isoperimetric inequality. We propose several geometric evolution equations to prove this inequalities. The problem is reduced to a parabolic fully nonlinear PDE. 

29th Jan. Agnieszka Kalamajska. Institute of Mathematics. Warsaw University. 1pm. Old Chem 807. 

`On modifications of weakly convergent sequences of gradients'   Abstract


5th Feb. Andres Bjorn. Linkoping University, Sweden. 1pm. Old Chem 807. 

`Cluster set for Sobolev (Newtonian) functions and quasiminimizers'

Abstract: Cluster sets have been used in many situations to describe boundary behavior when a function does not have a limit (it is by definition the set of all limit values the function takes along different sequences towards the boundary point). As far as I know it has only been studied in connections with continuous functions. 

In this talk I will discuss (essential) cluster sets for Sobolev functions.I will present some results on when the cluster set is connected and when it takes a prescribed boundary value. It turns out that this is true in quite general metric spaces, and there are close connections with some fine properties of Newtonian functions that Jana Bj\"orn has talked about. The talk is nevertheless accessible also to those who has not attended Jana's course.

Finally I will apply the results to quasiminimizers, which are generalizations of p-harmonic functions, and briefly discuss some of their boundary regularity.



------------------------------- Past Seminars -----------------------------

Fall Quarter 2009. (Usually) Fridays at 1pm. 801 Old Chem.

8th October. Michael Goldberg. 1pm 702 Old Chem.
`Harmonic Analysis in the Schroedinger equation'

30th October. Robbie Buckingham. 1pm Room 801. Old Chem.                        

'Analysis of the sin-Gordon equation using the inverse scattering method'


  20th November. Leonid Slavin. 1pm R00m 801. Old Chem. 
 'Bellman functions for the dyadic maximal operator. Part 1'

 4th Dec. Jesus Jaramillo. Universidad Complutense de Madrid 
`Global inversion theorems and covering maps of lenght spaces'

Abstract: We first review some classical results about global inversion of  smooth manifolds. We also stress the connection with covering maps. Then  we present some  recent results where conditions are given for a local homeomorphism between length metric spaces to be a covering map. Some  applications are given to the case of mappings between Finsler  manifolds.


Spring Quarter 2009. (Usually) Thursdays at 1pm. 605 Old Chem.

16th of April. Riika Korte, University of Helsinki.

`Characterizations for Hardy inequalities'.

24th of April. Stephen Semmes, Rice University.

`Very Happy Fractals'. 316 Braunstein. 3pm


30th of April. Andrew Lorent.

`Gamma convergence and the Aviles Giga functional I'.


7th of May. Andrew Lorent

`Gamma convergence and the Aviles Giga functional II'.

14th of May. Changyou Wang. University of Kentucky

`Boundary regularity for biharmonic maps between manifolds'


22nd of May (Friday) 1pm. Niko Marola. University of Helsinki.

`On Beckenbach-Rado type integral inequalities'. In Swift 719.

Abstract: Beckenbach and Rado characterized logarithmically subharmonic functions in the plane in terms of integral inequalities involving spherical averages. In this talk we generalize this result to higher dimensions and thus answer to a question raised by Beckenbach and Rado. We also consider generalizations of integral inequalities suggested by Beckenbach and Rado and discuss connections to reverse Holder inequalities and Muckenhoupt weights.

5th of June, 1pm. David Minda.

`Conformal automorphisms of plane regions'



------------------------------- Past Seminars -----------------------------

Winter Quarter. Thursdays at 1pm. 809 Swift Hall.

15th Jan. Bingyu Zhang . `Applications of Harmonic Analysis to Nonlinear Dispersive Wave Equation I'. Slides

12th Feb. Bingyu Zhang . `Applications of Harmonic Analysis to Nonlinear Dispersive Wave Equation 2'. 809 Swift Hall.

19th Feb. Xiangdong Xie. Georgia Southern.

`Quasiisometric rigidity and quasisymmetric extension'.809 Swift Hall.

Abstract: I will discuss the following two questions:

1. Is every quasiisometry between two Hadamard manifolds at a finite distance from a bilipschitz map?
2. When does a (power) quasisymmetry between the boundaries of two Euclidean domains extend to a quasisymmetry between the domains?
I shall prove that the answer to question 1 is positive when the Hadamard manifolds are the universal covers of compact manifolds with negative curvature.


26th Feb. Nages Shanmugalingam `Besov spaces and traces

theorems in metric spaces I'.809 Swift Hall.

5th March. Nages Shanmugalingam `Besov spaces and traces

theorems in metric spaces II'.809 Swift Hall.


Fall Quarter, 2008.

9th Oct. Nages Shanmugalingam `Planar BV extension domains'

16th Oct. Andrew Lorent `Liouville theorem's old and new, part 1'

23rd Oct. Andrew Lorent `Liouville theorem's old and new, part 2'


30th Oct. Tomasz Adamowicz. `On the p-harmonic world, part 1'


6th Nov. Tomasz Adamowicz. `On the p-harmonic world, part 2'

21st Nov. 2pm-3pm. Pekka Panka.

`Finite distortion, value distribution, and cohomology'

Abstract: The Mattila-Rickman equidistribution theorem implies that a geometrically controlled branched covering map (i.e, a quasiregular mapping) into a closed manifold must visit every set as often as its relative size indicates. I will discuss this corollary for more general branched covering maps (mappings of finite distortion). This result is a key ingredient in a cohomological boundedness theorem for closed manifolds admitting entire mappings of bounded mean distortion.


25th Nov. 3pm-4pm. 708 Old Chem. John Lewis

`Applications of Boundary Harnack Inequalities for p Harmonic Functions'. 

Abstract

11th Dec. Davis Minda. `Stretching convex regions and the hyperbolic metric'



Subpages (1): Agnieszka abstract