Volume of nodal sets of eigenfunctions

Speaker: 

Hamid Hezari

Institution: 

UC Irvine

Time: 

Friday, December 7, 2012 - 4:00pm

Location: 

MSTB 120

Yau's conjecture states that the volume of the nodal set of
Laplace eigenfunctions on a compact Riemannian manifold is comparable to
the square root of the corresponding eigenvalue. Donnelly and Fefferrman
proved Yau's conjecture for real analytic metrics but the conjecture stays
widely open for smooth metrics specially in dimensions n>2. Recently
Sogge-Zelditch and Colding-Minicozzi have established new lower bounds for
the volume of the nodal sets. In this talk we give a new proof of
Colding-Minicozzi's result using a different method. This is a joint work
with Christopher Sogge and Zuoqin Wang.

Mathematical quasicrystals and their spectral properties

Speaker: 

Anton Gorodetski

Institution: 

UC Irvine

Time: 

Friday, November 30, 2012 - 4:00pm

Location: 

MSTB 120

Penrose tilings and substitution sequences, spectral properties of operators in Hilbert space and dynamical systems, fractals and convolutions of singular measures - we will see how all these topics meet in the study of mathematical quasicrystals. 

Curve shortening: an introduction to geometric evolutions

Speaker: 

Jeff Streets

Institution: 

UC Irvine

Time: 

Friday, October 12, 2012 - 4:00pm to 5:00pm

Location: 

MSTB 120

What happens when we decrease the length of a closed curve in
the plane as fast as possible? This seemingly simple question has a very
nice answer which involves a beautiful combination of partial differential
equations and planar geometry. Come and get a glimpse of the amazing
subject of geometric flows!

Non-allosteric ultrasensitive responses in signal transduction

Speaker: 

German Enciso

Institution: 

UC Irvine

Time: 

Friday, October 28, 2011 - 4:00pm

Location: 

mstb 120

A key phenomenon in the study of cell-to-cell communication and
protein regulation is the all-or-none, ultrasensitive dose response, which
transforms a continuous input into a digital output. Multisite systems are
often used in conjunction with allosteric effects to create such a behavior.
In this talk I describe a non-allosteric mechanism for a multisite system to
present strongly ultrasensitive behavior. Applications are given to protein
activation through multisite phosphorylation, clusters of receptors and DNA
regulation through histone modifications.

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