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# Differential Geometry (Leader: Dr. Diego Ricciotti <ricciotti (at) usf.edu>document.write('<a href="mai' + 'lto:' + 'ricciotti' + '&#64;' + 'usf.edu' + '">Dr. Diego Ricciotti</a>');)

## Friday, April 19, 2019

Title
Speaker
Time
Place

Randomness in the Heisenberg group
Diego Ricciotti
12:30pm-1:30pm
CMC 109

Abstract

We discuss some stochastic processes and their relation to Brownian motion and PDEs in the Heisenberg group.

## Friday, April 12, 2019

Title

Speaker
Time
Place

A new proof for the equivalence of weak and viscosity solutions for the $$p$$-Laplace and the $$p(x)$$-Laplace equation in $$R^n$$
Robert Freeman
12:30pm-1:30pm
CMC 109

Abstract

The equivalence of weak and viscosity solutions in $$R^n$$ was given by Juutinen, Lindqvist, and Manfredi in 2001. In this talk we will examine the new proof of the equivalence for the $$p$$-Laplace equation in $$R^n$$ via infimal convolutions given by Julin and Juutinen in 2012. We will also discuss the strategies/difficulties in extending this proof to the $$p(x)$$-Laplace equation in R^n as well as the Heisenberg group.

## Friday, April 5, 2019

Title
Speaker
Time
Place

Tug of war games and the p-Laplacian in the Heisenberg group
Diego Ricciotti
12:30pm-1:30pm
CMC 109

Abstract

We discuss a game theoretic interpretation of $$p$$-harmonic functions by exploiting the connection between PDEs, mean value properties and dynamic programming principles. In particular we obtain an approximation scheme at a discrete level, and we prove uniform convergence to the solution of the associated Dirichlet problem with continuous boundary datum, under suitable regularity assumptions of the domain.

## Friday, March 22, 2019

Title
Speaker
Time
Place

Equivalence of weak and viscosity solutions to the $$p(x)$$-Laplace equation in Carnot groups
Robert Freeman
12:30pm-1:30pm
CMC 109

Abstract

We will discuss the known Euclidean results and new results in Carnot groups of the equivalence of weak and viscosity solutions to the $$p(x)$$-Laplace equation.

## Friday, March 15, 2019

No seminar this week due to Spring Break.

## Friday, February 22, 2019

Title
Speaker
Time
Place

Nonlinear potential theory, Part 1
Thomas Bieske
12:30pm-1:30pm
CMC 109

Abstract

We discuss various topics in nonlinear potential theory from Heinonen-Kilpelainen-Martio such as $$A_p$$ weights, quasiconformal mappings and capacity of sets.

## Friday, February 15, 2019

Title
Speaker
Time
Place

Plates with incompatible prestrain and non-euclidean elasticity
Diego Ricciotti
12:30pm-1:30pm
CMC 109

Abstract

We examine a model (coming from non-Euclidean elasticity) for thin plates that become internally prestrained in the absence of external forces or imposed boundary conditions. Examples of this phenomena occur in nature for instance in growing leaves or tissues. We describe a derivation of a 2D model arising as $$\Gamma$$-limit of a 3D model as the thickness parameter approaches zero, under appropriate scalings of the energy in terms of the plate's thickness.

## Friday, February 8, 2019

Title
Speaker
Time
Place

Sub-Riemannian Geometry and Partial Differential Equations, Part IV
Thomas Bieske
12:30pm-1:30pm
CMC 109

## Friday, February 1, 2019

Title
Speaker
Time
Place

Sub-Riemannian Geometry and Partial Differential Equations, Part III
Thomas Bieske
12:30pm-1:30pm
CMC 109

## Friday, January 25, 2019

Title
Speaker
Time
Place

Sub-Riemannian Geometry and Partial Differential Equations, Part II
Thomas Bieske
12:30pm-1:30pm
CMC 109

## Friday, January 18, 2019

Title
Speaker
Time
Place

Sub-Riemannian Geometry and Partial Differential Equations
Thomas Bieske
12:30pm-1:30pm
CMC 109

Abstract

We examine properties of solutions to the eikonal and infinite Laplace equations in sub-Riemannian spaces. The interplay between the underlying geometry and these solutions will also be explored.