Prof. U. B. Tewari Distinguished Lecture Series in Mathematics
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
Speaker: Prof. Pertti Mattila, University of Helsinki
Title: Applications of the Fourier transform to Hausdorff dimension
Date: 7,8,9,11 November 2024
Time: 03:30 PM (IST)
Venue: LH-14
Brochure: UBT-Lecture Series-Brochure
Abstract:
Starting from Kaufman's work in 1968 and Falconer's
in 1982 on orthogonal projections of general Borel sets, there have been
many applications of the Fourier transform to geometric problems
involving Hausdorff dimension.
In addition to orthogonal projections, such topics include Hausdorff
dimension of line sections, of intersections of Borel sets in general
positions, and of distance sets. During roughly the last ten years r e l
a t e d q u e s t i o n s o n r a d i a l projections have been studied
intensively by Orponen, Shmerkin and others. This work is connected with
the Furstenberg set problem and has been a partial ingredient in its
recent solution by Ren and Wang. There are also connections to the
Kakeya problem. The lectures will aim to give an overview of some of the
results, methods and ideas in this scenario.
About the Series:
The lecture series is in honour of Prof. U. B. Tewari (1944-2019) for his outstanding contributions in mathematics. This annual event is generously established by his family, friends, and former students. Each year, a distinguished mathematician is invited to deliver a comprehensive short course consisting of 4-5 lectures spread over a two-week period in a forefront area of Mathematics. This year's lecture is the third in the series, and it includes a short course designed to engage researchers and graduate students. All the lectures will be in hybrid mode.
About the Speaker:
Pertti
Mattila is a Finnish mathematician and a leading figure in geometric
measure theory and fractal geometry. His pioneering contributions
continue to influence ongoing research and shape the future directions
of harmonic analysis, complex analysis, and geometric measure theory. He
has explored the geometric and measure-theoretic properties of fractal
sets, contributing significantly to the development of this rich and
intricate field. Mattila is the author of several influential books and
numerous research papers. His books "Geometry of Sets and Measures in
Euclidean Spaces: Fractals and Rectifiability" and "Fourier Analysis and
Hausdorff Dimension" are widely cited.
Pertti Mattila obtained his Ph.D. in Mathematics from the University of
Helsinki in 1973. He has held academic positions at various
institutions, including a postdoctoral position at the Institute for
Advanced Study at Princeton University, and professorships at the
University of Jyväskylä and the University of Helsinki. Currently, he is
part of the Centre of Excellence in Analysis and Dynamics Research at
the University of Helsinki. He has been invited to speak at numerous
international conferences, including the International Congress of
Mathematicians (ICM) in Berlin in 1998, and has received several awards
and honors for his work, including the Magnus Ehrnrooth Foundation Prize
(2000), given by Finnish Society of Science and Letters.
About Prof. U. B. Tewari:
Prof
U. B. Tewari, popularly known as UBT, obtained his Ph.D at the
University of California Berkeley, and joined IIT Kanpur in 1970. He was
known for his inspiring and rigorous teaching. He started an Harmonic
Analysis School at IITK and brought together colleagues from other
reputed institutes in India. Prof. Tewari has received many awards,
including the Shanti Swaroop Bhatnagar Prize, and the Meghnad Saha award
for research in Theoretical Sciences. He was also a Fellow of the
National Academy of Sciences, Allahabad.