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Program:
All lectures are on Thursdays from 16:00-17:00,
unless otherwise stated.
May 24
Snellius B1.
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Filmvertoning:
Late style - Yuri I. Manin Looking Back on a Life in Mathematics
Studievereniging De Leidsche Flesch zal de onlangs verschenen biografische documentaire "Late Style - Yuri I. Manin Looking Back on a Life in Mathematics" vertonen gemaakt door Agnes Handwerk en Harrie Willems. Late Style vertelt het verhaal over Yuri Manin tijdens de gouden jaren van de wiskunde in Moskou tijdens de jaren zestig en zeventig - een periode die niet alleen in het teken van de wiskunde stond, maar zeker ook beïnvloed werd door de plitieke situatie in Rusland. Voorafgaand aan de filmvertoning zal Frans Oort een introductie geven.
Programma: 15:45 koffie en thee, 16:00 inleiding Frans Oort, 16:30 vertoning "Late Style"
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May 10, 2012
Snellius 174.
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Sander Dahmen (Utrecht):
Solving Diophantine equations: the modular method
Abstract.
Since the proof of FLT, many Diophantine problems have been solved
using deep results about elliptic curves, modular forms, and
associated Galois representations. The purpose of this talk is to
discuss some of these results and explain how they can be applied to
explicitly solve certain Diophantine equations. We shall focus in
particular on so-called generalized superelliptic equations, i.e.
exponential Diophantine equations of the form F(x,y)=z^n where F is a
binary form over the integers (to be solved in integers x,y,z,n with
n>1 and x and y coprime).
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April 26, 2012
Snellius 174.
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Roeland Merks (CWI & Leiden):
Modeling stochastic self-organization of multicellular tissues: on the growth of blood vessels and glands
Abstract.
Morphogenesis, the formation of biological shape and pattern during embryonic development, is a topic of intensive experimental investigation, so the participating cell types and molecular signals continue to be characterized in great detail. Yet this only partly tells biologists how molecules and cells interact dynamically to construct a biological tissue. Mathematical and computational modeling are a great help in answering such questions on biological morphogenesis. Cell-based simulation models of blood vessel growth describe the behavior of cells and the signals they produce. They then simulate the collective behavior emerging from these cell-cell interactions. In this way cell-based models help analyze how cells assemble into biological structures, and reveal the microenvironment the cells produce collectively feeds back on individual cell behavior. In this way, our simulation models, based on a Cellular Potts model combined with partial-differential equations, have shown that the elongated shape of cells is key to correct spatiotemporal in silico replication of vascular network growth. The models have also helped identify a new stochastic mechanism for the formation of branched structures in epithelial gland tissues. I will discuss some recent insights into these mechanisms. Then I will discuss our more recent cell-based modeling studies of cell-extracellular matrix interactions during angiogenesis. I will conclude by suggesting some interesting continuum and stochastic mathematical problems that our cell-based simulations suggest.
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April 19, 2012
Snellius 174.
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Anthony Wickstead (Queen's University Belfast):
The Riesz Decomposition Property for some spaces of real-valued functions
Abstract.
An ordered space V has the Riesz Separation Property (RSP) if
f_1, f_2, h_1, h_2 \in V and f_1, f_2 \leq h_1, h_2 implies there is a g in V with f_1, f_2 \leq g \leq h_1, h_2.
Many, but not all, interesting vector spaces of functions have the RSP
even though they do not possess the stronger property of being a
vector lattice. The talk will survey results on this topic due to H.H.
Schaefer, L. Fuchs and A. Nagel & W. Rudin.
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March 22, 2012
Snellius 174.
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André Henriques (Utrecht):
What is an elliptic object?
Abstract.
Elliptic cohomology (also called "topological modular forms" of "TMF")
is a cohomology theory that was constructed in the 90ties by homotopy
theoretical means.
Several strong indicators make people believe that there exist
geometric objects that represent elliptic cohomology classes. However,
despite multiple attempts by many people, nobody has managed to
define those elusive "elliptic objects".
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February 23, 2012
Snellius 174
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John F. Bukowski (Juniata College & Leiden):
The Diverse Interests of Christiaan Huygens: Mechanics and Music
Abstract.
Christiaan Huygens contributed to the early history of the problem of the hanging chain when he proved at age 17 that the chain did not take the shape of a parabola. We will examine his proof in detail. Huygens was also one of many seventeenth-century mathematicians interested in the tuning of the musical scale. We will see how he used logarithms to divide the octave into a 31-tone scale, and we will compare his tuning to other tunings of the scale.
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