The UCF Mathematics Colloquium, held every Monday from 3:30 to 4:30 p.m. in MSB 318, offers a diverse platform for research scholars, faculty, students, and industry experts to share and exchange ideas, fostering discussion and networking across various areas of mathematics.
Professor Ugur Abdulla from Okinawa Institute of Science and Technology, Japan will speak at this week's colloquium on Kolmogorov Problem and Wiener-type Criteria for the Removability of the Fundamental Singularity for the Elliptic and Parabolic PDEs.
Abstract: This talk will address the major problem in the Analysis of PDEs on the nature of singularities reflecting the natural phenomena. I will present my solution of the Kolmogorov's Problem (1928) expressed in terms of the new Wiener-type criterion for the removability of the fundamental singularity for the heat equation. The new concept of regularity or irregularity of singularity point for the parabolic (or elliptic) PDEs is defined according to whether or not the caloric (or harmonic) measure of the singularity point is null or positive. The new Wiener-type criterion precisely characterizes the uniqueness of boundary value problems with singular data, reveal the nature of the harmonic or caloric measure of the singularity point, asymptotic laws for the conditional Brownian motion, and criteria for thinness in minimal-fine topology. The talk will be oriented to a general audience including non-expert faculty and graduate students.
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