SMS Distinguished Visitor Programme (DVP)
2019
Programme 
Distinguished
Visitor Programme (DVP) 

Audience 
General 

Description 
The Distinguished Visitor
Programme was launched by the Singapore Mathematical Society in 1998. Through
the visit of a distinguished mathematician/mathematics educator, who will
interact with both mathematicians/mathematics educators at the universities
as well as teachers and pupils at the schools here, the aim of the Programme
is to expose as large and diverse an audience as possible to the excitement
and relevance of mathematics, thereby enhance the awareness of mathematics in
our society. 

Distinguished
Visitor 


Events 

Solutions
of SPDE as zeros of maps on scaled path spaces Joint work
with Viorel Barbu (Romanian Academy of Sciences, Iasi) It has been
recently shown that the solutions of a large class of stochastic partial
differential equations (SPDE) can be obtained as zeros of a properly defined
map on a path space equipped with a norm which is
“scaled” by the exponential of a functionvalued Brownian motion. In the talk this result will be reviewed and connected to current
developments about the case where the underlying SPDE is a gradient flow,
perturbed by linear multiplicative noise. In this case it follows from the
above result and by applying methods from the calculus of variations that the
solution minimizes a certain explicit convex functional on the path space.
Applications include stochastic porous media equations, stochastic nonlinear
parabolic equations (as e.g. the stochastic Cauchy problem for the
pLaplacian) and in the nongradient case also stochastic nonlinear transport
equations.
(No
registration required) 

Colloquium
Talk 2 
Nonlinear
FokkerPlanck equations and distribution dependent SDE It is a classical problem to present a solution of a PDE as the density
of the time marginal distributions of a stochastic process. If the PDE is a
linear FokkerPlanck equation, then by classical stochastic analysis this is
known to be true under very general conditions. For nonlinear FokkerPlanck
equations the situation is much more difficult and only known to be true
under very restrictive assumptions on the regularity of the (nonlinear)
dependence of the coefficients in the FokkerPlanck equations on the
solutions. In this talk a new general concept is presented, how to find the
desired stochastic process (similarly as in the linear case) through solving
a corresponding stochastic differential equation (SDE), whose coefficients,
however, depend on the marginal distributions of its solution (DDSDE). The
point is that this new general concept does not require strong regularity
assumptions on the coefficients (as e.g. fulfilled for McKeanVlasov type
equations) and thus does not rule out a lot of other nonlinear ForkerPlanck
equations of interest in Physics. As an example it will be shown that it can
be applied to the case, where the nonlinear FokkerPlanck equation is a
generalized porous media equation on ddimensional Euclidean space (with d
arbitrary), perturbed by a transport term. So its solution is the density of
the time marginal distributions of a (tractable) stochastic process solving a
corresponding DDSDE. Apart from its conceptual interest this result could
lead to new numerical approximations of solutions to nonlinear FokkerPlanck
equations through numerically solving the corresponding DDSDE. In the first part of the talk, we shall recall the general connection
between stochastic differential equations and (both linear and nonlinear)
FokkerPlanck equations. Target
Audience: Mathematicians
and Researchers (No
registration required) 
Finding Order in Disorder: Mathematics is Everywhere The lecture will present an example of a topic in mathematics which is rooted in elementary school mathematics, materializes later again in high school as well as in university mathematics and finally turns out to be a part of current mathematical research with striking applications, for example in modeling dynamical processes in finance or climatology. Another aim of the lecture is to convince the audience that in order to really understand our environment, both in its phenomenological and quantitative analysis, one has to take into account the influence of randomness.
Target Audience: General public Please register here 



Registration
Fees: 
Free 
Coordinator: 