9:00am to 10:00am - Zoom - Inverse Problems Ru-Yu Lai - (University of Minnesota) An inverse problem for the Boltzmann equation |
10:00am to 11:00am - zoom https://uci.zoom.us/j/93076750122?pwd=Y3pLdndoQTBuNUhxQUxFMkQ2QnRFQT09 - Mathematical Physics Oleg Safronov - (UNCC) Relations between discrete and continuous spectra of differential operators We will discuss relations between different parts of spectra of differential operators. In particular, we will see that negative and positive spectra of Schroedinger operators are related to each other. However, there is a stipulation: one needs to consider two operators one of which is obtained from the other by flipping the sign of the potential at each point x. If one knows only that the negative spectra of the two operators are discrete, then their positive spectra do not have gaps. If one knows more about the rate of accumulation of the discrete negative eigenvalues to zero, then one can say more about the absolutely continuous component of the positive spectrum. |
3:00pm - Zoom https://uci.zoom.us/j/97940217018 - Number Theory Geoffrey Akers - (CUNY Graduate Center) On a universal deformation ring that is a discrete valuation ring We consider a crystalline universal deformation ring R of an n-dimensional, mod p Galois representation whose semisimplification is the direct sum of two non-isomorphic absolutely irreducible representations. Under some hypotheses, we obtain that R is a discrete valuation ring. The method examines the ideal of reducibility of R, which is used to construct extensions of representations in a Selmer group with specified dimension. This can be used to deduce modularity of representations. |
4:00pm - Zoom https://zoom.us/j/8473088589 - Graduate Seminar Abel Klein - (UC Irvine) TBA |