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UID:www.tcs.tifr.res.in/event/891
DTSTAMP:20230914T125942Z
SUMMARY:On Randomization and Combinatorics in Computational Geometry\, Disc
rete Mathematics\, and Combinatorial Representation Theory.
DESCRIPTION:Speaker: Kunal Dutta (Max Planck Institute for Informatics\nSaa
rland Informatics Campus\nBuilding E1 4\n66123 Saarbrücken\nGermany)\n\nA
bstract: \nAbstract: In this talk we shall see three very different areas
of applications of combinatorics in mathematics and computer science\, i
llustrating different flavours of combinatorial reasoning.\n\nFirst\, we c
onsider lower bounds on the maximum size of an independent set\, as well a
s the number of independent sets\, in k-uniform hypergraphs\, together wit
h an extension to the maximum size of a subgraph of bounded degeneracy in
a hypergraph. Joint works with C. R. Subramanian (IMSc\, Chennai)\, Dhruv
Mubayi (UIC\, Chicago) and Jeff Cooper (UIC\, Chicago) and Arijit Ghosh (I
MSc Chennai).\nNext\, we shall look at Haussler's Packing Lemma from Compu
tational Geometry and Machine Learning\, for set systems of bounded VC di
mension. We shall go through its generalization to the Shallow Packing Le
mma for systems of shallow cell complexity\, and see how it can be used t
o prove the existence of small representations of set systems\, such as e
psilon nets\, M-nets\, etc. Joint works with Arijit Ghosh (IMSc\, Chenn
ai)\, Nabil Mustafa (ESIEE Paris)\, Bruno Jartoux (ESIEE Paris) and Esthe
r Ezra (Georgia Inst. Tech.\, Atlanta).\nThe last problem is on the decom
position\, into irreducible representations\, of the Weil representation
of the full symplectic group associated to a finite module of odd order o
ver a Dedekind domain. We shall discuss how a poset structure defined on
the orbits of finite abelian p-groups under automorphisms can be used to
show the decomposition of the Weil representation is multiplicity-free\,
as well as parametrize the irreducible subrepresentations\, compute their
dimensions in terms of p\, etc. Joint works with Amritanshu Prasad (IMSc
\, Chennai).\n
URL:https://www.tcs.tifr.res.in/web/events/891
DTSTART;TZID=Asia/Kolkata:20180720T140000
DTEND;TZID=Asia/Kolkata:20180720T150000
LOCATION:A-201 (STCS Seminar Room)
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