BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Owen Gwilliam (UMass)
DTSTART;VALUE=DATE-TIME:20200930T193000Z
DTEND;VALUE=DATE-TIME:20200930T203000Z
DTSTAMP;VALUE=DATE-TIME:20240328T214122Z
UID:penncolloquium/1
DESCRIPTION:Title: Spontaneous symmetry breaking\, a view from derived geometry\nb
y Owen Gwilliam (UMass) as part of UPenn Mathematics Colloquium\n\n\nAbstr
act\nWe will give an overview of how physics and homological algebra have
met in the setting of gauge theory\, with an emphasis on how the new subje
ct of derived geometry provides a clarifying framework. The talk's concret
e aim is to explain the Higgs mechanism as a case study. Our approach will
be low-tech and will emphasize the motivations\; anyone familiar with not
ions like vector bundle and cochain complex should be able to follow.\n
LOCATION:https://researchseminars.org/talk/penncolloquium/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Simpson (Nice\, visiting IAS)
DTSTART;VALUE=DATE-TIME:20201014T193000Z
DTEND;VALUE=DATE-TIME:20201014T203000Z
DTSTAMP;VALUE=DATE-TIME:20240328T214122Z
UID:penncolloquium/2
DESCRIPTION:Title: Classification of finite algebraic objects\nby Carlos Simpson (
Nice\, visiting IAS) as part of UPenn Mathematics Colloquium\n\n\nAbstract
\nI'll report on my current work in progress about the classification of s
emigroups and finite categories. This will include a quick introductionto
neural networks\, and a discussion of how they can help in the classificat
ion proofs. We'll also look at some potential applications to construction
problems in algebraic geometry.\n
LOCATION:https://researchseminars.org/talk/penncolloquium/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Bamler (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20201028T193000Z
DTEND;VALUE=DATE-TIME:20201028T203000Z
DTSTAMP;VALUE=DATE-TIME:20240328T214122Z
UID:penncolloquium/3
DESCRIPTION:Title: Recent developments in Ricci flow\nby Richard Bamler (UC Berkel
ey) as part of UPenn Mathematics Colloquium\n\n\nAbstract\nRicci flows are
a powerful geometric-analytical tool\, as they have been used to prove im
portant results in low-dimensional topology. \n\n \n\nIn the first part of
this talk I will focus on Ricci flows in dimension 3. I will briefly revi
ew Perelman’s construction of Ricci flow with surgery\, which led to the
resolution of the Poincar\\’e and Geometrization Conjectures. Then I wi
ll discuss recent work of Lott\, Kleiner and myself on an improved version
of this flow\, called “singular Ricci flow”. This work allowed us to
resolve the Generalized Smale Conjecture\, concerning the structure of dif
feomorphism groups\, and a conjecture concerning the contractibility of th
e space of positive scalar curvature metrics on 3-manifolds.\n\n \n\nIn th
e second part of the talk\, I will focus on Ricci flows in higher dimensio
ns. I will present a new compactness\, which can be used to study the sing
ularity formation of the flow\, as well as its long-time asymptotics. I wi
ll discuss these and some further consequences. I will also convey some in
tuition of the new terminology that had to be introduced in connection wit
h this compactness theory.\n
LOCATION:https://researchseminars.org/talk/penncolloquium/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benson Farb (U Chicago)
DTSTART;VALUE=DATE-TIME:20201202T203000Z
DTEND;VALUE=DATE-TIME:20201202T213000Z
DTSTAMP;VALUE=DATE-TIME:20240328T214122Z
UID:penncolloquium/4
DESCRIPTION:Title: Hilbert's 13th problem\nby Benson Farb (U Chicago) as part of U
Penn Mathematics Colloquium\n\n\nAbstract\nHilbert's 13th Problem (H13) is
a fundamental open problem about polynomials in one variable. It is part
of a beautiful (but mostly forgotten) story going back 3 thousand years.
In this talk I will explain how H13 (and related problems) fits into a wi
der framework that includes problems in enumerative algebraic geometry and
the theory of modular functions. I will then report on some recent progre
ss\, joint with Mark Kisin and Jesse Wolfson. While some fancy objects wi
ll appear in this talk\, much of it should (I hope) be understandable to u
ndergraduate math majors.\n
LOCATION:https://researchseminars.org/talk/penncolloquium/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksandr Logunov (Princeton)
DTSTART;VALUE=DATE-TIME:20210127T203000Z
DTEND;VALUE=DATE-TIME:20210127T213000Z
DTSTAMP;VALUE=DATE-TIME:20240328T214122Z
UID:penncolloquium/5
DESCRIPTION:Title: Zero sets of Laplace eigenfunctions\nby Aleksandr Logunov (Prin
ceton) as part of UPenn Mathematics Colloquium\n\n\nAbstract\nIn the begin
ning of 19th century Napoleon set a prize for the best mathematical explan
ation of Chladni’s resonance experiments. Nodal geometry studies the zer
oes of solutions to elliptic differential equations such as the visible cu
rves that appear in these physical experiments. We will discuss geometrica
l and analytic properties of zero sets of harmonic functions and eigenfunc
tions of the Laplace operator. For harmonic functions on the plane there i
s an interesting relation between local length of the zero set and the gro
wth of harmonic functions. The larger the zero set is\, the faster the gro
wth of harmonic function should be and vice versa. Zero sets of Laplace ei
genfunctions on surfaces are unions of smooth curves with equiangular inte
rsections. Topology of the zero set can be quite complicated\, but Yau con
jectured that the total length of the zero set is comparable to the square
root of the eigenvalue for all eigenfunctions. We will start with open qu
estions about spherical harmonics and will explain some methods to study n
odal sets.\n
LOCATION:https://researchseminars.org/talk/penncolloquium/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathryn Hess (École Polytechnique Fédérale de Lausanne)
DTSTART;VALUE=DATE-TIME:20210210T203000Z
DTEND;VALUE=DATE-TIME:20210210T213000Z
DTSTAMP;VALUE=DATE-TIME:20240328T214122Z
UID:penncolloquium/6
DESCRIPTION:Title: Trees\, barcodes\, and symmetric groups\nby Kathryn Hess (Écol
e Polytechnique Fédérale de Lausanne) as part of UPenn Mathematics Collo
quium\n\n\nAbstract\nMotivated by the desire to automate classification of
neuron morphologies\, we designed a topological signature\, the Topologic
al Morphology Descriptor (TMD)\, that assigns a barcode to any geometric
tree (i.e\, any finite binary tree embedded in R^3). We showed that the TM
D effectively determines the reliability of clusterings of random and neur
onal trees. Moreover\, using the TMD we performed an objective\, stable cl
assification of pyramidal cells in the rat neocortex\, based only on the s
hape of their dendrites.\nWe have also reverse-engineered the TMD\, in ord
er to digitally synthesize dendrites\, to compensate for the dearth of ava
ilable biological reconstructions. The algorithm we developed\, called Top
ological Neuron Synthesis (TNS)\, stochastically generates a geometric tre
e from a barcode\, in a biologically grounded manner. The synthesized cort
ical dendrites are statistically indistinguishable from the corresponding
reconstructed dendrites in terms of morpho-electrical properties and the n
etworks they form. We synthesized cortical networks of structurally altere
d dendrites\, revealing principles linking branching properties to the str
ucture of large-scale networks.\nIn this talk I will provide an overview o
f the TMD and the TNS and then describe the results of our theoretical and
computational analysis of their behavior and properties\, in which symmet
ric groups play a key role. In particular\, I will specify the extent to
which the TNS provides an inverse to the TMD. \nThis is joint work with Ad
élie Garin and Lida Kanari\, building on earlier collaborations led by Li
da Kanari.\n
LOCATION:https://researchseminars.org/talk/penncolloquium/6/
END:VEVENT
END:VCALENDAR