Spring 2025
Organized by Mihaela Vajiac and Polona Durcik, sponsored by CECHA.
The talks will be held in a hybrid format, on Zoom and/or on campus at Keck Center of Science and Technology (no. 30 on the Campus map, at the intersection of Walnut Ave and Center St).
Zoom: https://chapman.zoom.us/j/99396752824
(Meeting ID: 993 9675 2824)
Schedule
Friday, May 23, 11am-noon, Keck Center 370
Joris Roos (University of Massachusetts Lowell)
Spherical maximal functions and fractal dimensions
Abstract: The talk will be about spherical maximal functions with a supremum restricted to a given set E. The sharp L^p improving regions of these operators depend on various fractal dimensions of the set E such as the Minkowski dimension, quasi-Assouad dimension and certain intermediate dimensions. A surprising aspect is that the sharp exponent regions need not be polygons; instead their boundary may follow an arbitrary convex curve in some critical region. The talk will be about some old and some new results. If time allows, we will also discuss a related fractal variant of the local smoothing problem for the wave equation.
Monday, May 19, 1-2pm, Hashinger 222 (please note the change of building)
H. Turgay Kaptanoglu (Bilkent University, Ankara, Turkey)
Extremal Problems in Weighted Bergman-Besov Spaces through Bergman Projections
Abstract: We extend the method of using Bergman projections for solving extremal problems introduced by Ferguson to systematically compute extremal functions in weighted Bergman-Besov spaces at arbitrary data points in the unit disc. We include the case p=1 by first proving the existence of solutions to a large class of extremal problems in this case. We also develop expansions of analytic functions in terms of Mobius factors similar to Taylor series to handle data points different from the origin. Our method is especially suitable for Caratheodory-Fejer-type interpolation.
Friday, May 16, 3-4pm, Keck Center 149
Serap Oztop (Istanbul University, Istanbul, Turkey)
Orlicz Amalgam Spaces and Algebras
Abstract: Let G be a locally compact group, Φ1,Φ2 be Young functions and ω be a moderate weight function on G. We introduce the weighted Orlicz amalgam spaces W (LΦ1 (G), LΦ2 (G)) defined on G, where the local component space is the Orlicz space LΦ1(G) and the global component is the weighted Orlicz space LΦ2 (G). We prove that W (LΦ1 (G), LΦ2 (G)) is a Banach algebra with respect to convolution and investigate its properties. We extend the analysis concerning classical Lebesgue amalgam spaces and Banach algebras to Orlicz amalgam algebras. We are also interested in inclusion relations between the Orlicz amalgam spaces W(LΦ1(G),LΦ2(G)) with respect to Young functions and weights. Among other things, we show that the inclusion relations among the local components imply inclusion relations for the amalgams. This talk is based on joint work with Büsra Aris.
Friday, February 7, 2025, 3:00pm - 4:30pm, Keck Center 156
Gigliola Stafillani (MIT)
What do I see from my corner of wave turbulence theory?
Abstract: Wave turbulence theory is a vast subject and its goal is to formulate for us a multiscale picture of wave interactions. Phenomena involving interactions of waves happen at different scales and in different media: from gravitational waves to the waves on the surface of the ocean, from our milk and coffee in the morning to infinitesimal particles that behave like wave packets in quantum physics. These phenomena are difficult to study in a rigorous mathematical manner, but because of this challenge, mathematicians have developed interdisciplinary approaches that are powerful and beautiful. I will describe some of these approaches and I will outline along the way questions that remain open in spite of the great progress already made.