SMS scnews item created by Miranda Luo at Tue 21 Jun 2022 1215
Type: Seminar
Distribution: World
Expiry: 27 Jun 2022
Calendar1: 27 Jun 2022 1700-1800
CalLoc1: Zoom webinar
Auth: miranda@w7r3b0j3.staff.wireless.sydney.edu.au (jluo0722) in SMS-SAML

# Asymptotic analysis of fractional problems via the logarithmic Laplacian

### Alberto Saldana

Dear friends and colleagues,

on Monday, 27 June 2022 at
03:00 PM for Beijing, Hong Kong and Perth
04:00 PM for Seoul and Tokyo
05:00 PM for Canberra, Melbourne and Sydney
07:00 PM for Auckland

Research Fellow Alberto Saldaña is giving a talk in our Asia-Pacific Analysis and PDE Seminar on

Asymptotic analysis of fractional problems via the logarithmic Laplacian

Abstract:

Fractional derivatives are commonly used to model a variety of phenomena, but... what does it mean to have a logarithmic derivative? And what would it be used for?

In this talk we focus on the logarithmic Laplacian, a pseudodifferential operator that appears as a first order expansion of the fractional Laplacian $$(-\Delta)^s$$ as the exponent $$s$$ goes to zero. This operator can also be represented as an integrodifferential operator with a zero-order kernel.

We will discuss how the logarithmic Laplacian can be used to study the behavior of linear and nonlinear fractional problems in the small order limit. This analysis will also reveal a deep and interesting mathematical structure behind the set of solutions of Dirichlet logarithmic problems.

Chair: Enrico Valdinoci (University of Western Australia)

More information and how to attend this talk can be found at the seminar webpage .

Miranda
On behalf of Daniel H. and Ben

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## Webinar Speaker

Alberto Saldaña
Research Fellow @ Universidad Nacional Autónoma de México

Alberto Saldaña studied financial mathematics in Mexico, where he also did a master in Mathematical Sciences. Later, he did a Ph.D. in Mathematics at Frankfurt University focused on the study of symmetries of solutions to parabolic and elliptic equations. Afterwards, Saldaña did three postdocs: one at the Free University of Brussels (ULB), another at Instituto Superior Técnico in Lisbon (IST), and the last one at the Karlsruhe Institute for Technology (KIT) in Germany. During this period he worked mostly in the existence theory and qualitative analysis of solutions to elliptic (local and nonlocal) problems. Since 2019, he has been an Associate Professor at the Institute of Mathematics of the National Autonomous University of Mexico (UNAM).