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SUMMARY:Marcelo VIANA (IMPA - Rio de Janeiro)
DTSTART;VALUE=DATE-TIME:20200527T130000Z
DTEND;VALUE=DATE-TIME:20200527T140000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171447Z
UID:ColloquiumDiDipartimento/1
DESCRIPTION:Title: Lyapunov exponents\nby Marcelo VIANA (IMPA - Rio de J
aneiro) as part of Colloquium del dipartimento di Matematica - Roma "Tor V
ergata"\n\n\nAbstract\nThe concept of Lyapunov exponent goes back to Lyapu
nov's 1892 thesis on the stability of differential equations\, and has num
erous applications in various branches of mathematics and science.\n\nStar
ting from the 1960s\, it found its proper mathematical framework in ergodi
c theory\, where it has had a prominent role ever since. In this colloquiu
m lecture I will review a few recent developments\, especially about the w
ay Lyapunov exponents depend on the underlying dynamical system.\n
LOCATION:https://researchseminars.org/talk/ColloquiumDiDipartimento/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Ghil (ENS and PSL University\, Paris\, and UCLA\, Los Ange
les)
DTSTART;VALUE=DATE-TIME:20200701T130000Z
DTEND;VALUE=DATE-TIME:20200701T140000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171447Z
UID:ColloquiumDiDipartimento/2
DESCRIPTION:Title: Nonautonomous and random dynamical systems in the climat
e sciences\nby Michael Ghil (ENS and PSL University\, Paris\, and UCLA
\, Los Angeles) as part of Colloquium del dipartimento di Matematica - Rom
a "Tor Vergata"\n\n\nAbstract\nH. Poincaré already raised doubts about th
e predictability of weather due to the divergence of orbits of dynamical s
ystems associated more recently with chaos. Progress in the theory of nonl
inear\, deterministic dynamical systems (DDS theory)\, on the one hand\, a
nd the highly ingenious work of E.N. Lorenz\, on the other\, justified Poi
ncaré’s early doubts. The theory of autonomous DDSs\, with time-indepen
dent forcing and coefficients\, provided a solid mathematical basis for mu
ch of the work on weather predictability over several decades.\nMore recen
tly\, an interesting and highly stimulating convergence occurred between s
tudies of climate predictability\, on the one hand\, and the development o
f the theory of nonautonomous and random dynamical systems (NDS and RDS)\,
on the other. The diurnal and the seasonal cycle of insolation played a s
omewhat limited role in weather predictability for 10–15 days\, but it b
ecame impossible to ignore the role of the seasonal cycle and of anthropog
enic effects in climate predictability for years to decades.\nAt the same
time\, the theory of purely deterministic\, skew product flows\, as well a
s that of RDSs\, incorporated time-dependent forcing and coefficients and
took huge mathematical strides\, including the rigorous formulation and ap
plication of pullback attractors. A parallel development in the physical l
iterature formulated and applied in a more intuitive fashion the closely r
elated concept of snapshot attractors.\nThese mathematical and physical ad
vances were seized upon by several groups of researchers interested in cli
mate modeling and predictability. In this talk\, I will try to present som
e of the mathematical background\, as well as some of the applications to
the climate sciences. These will include\, as time permits: (i) the use of
pullback and snapshot attractors for the proper understanding of the effe
cts of time-dependent forcing\, both deterministic and stochastic\, natura
l as well as anthropogenic\, upon intrinsic climate variability\; (ii) the
use of Wasserstein distance between time-dependent invariant measures to
estimate these effects\; (iii) the topological aspects of nonautonomous ef
fects upon the intrinsic variability\; and (iv) a “grand unification”
between the nonlinear\, deterministic and autonomous point of view espouse
d by E.N. Lorenz and the linear\, stochastically driven one of K. Hasselma
nn.\nThis talk reflects joint work with G. Charó\, M.D. Chekroun\, R. Dur
and\, A. DiGarbo\, Y. Feliks\, S. Galatolo\, F.-F. Jin\, D. Kondrashov\, V
. Lucarini\, L. Marangio\, J.D. Neelin\, S. Pierini\, D. Sciamarella\, E.
Simonnet\, Y. Sato\, J. Sedro\, L. Sushama\, and I. Zaliapin.\n
LOCATION:https://researchseminars.org/talk/ColloquiumDiDipartimento/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabrizio Catanese (University of Bayreuth)
DTSTART;VALUE=DATE-TIME:20201105T133000Z
DTEND;VALUE=DATE-TIME:20201105T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171447Z
UID:ColloquiumDiDipartimento/3
DESCRIPTION:Title: Nodal surfaces\, Coding theory\, and cubic discriminants<
/a>\nby Fabrizio Catanese (University of Bayreuth) as part of Colloquium d
el dipartimento di Matematica - Roma "Tor Vergata"\n\n\nAbstract\nNodal su
rfaces in 3-space are those surfaces whose singularities have nondegenerat
e Hessian. \nBasic numerical invariants are the degree d of a polynomial d
efining such a surface Y\, and the number \\nu of singular points. \nIf y
ou fix those integers (d\,\\nu) these surfaces are parametrized by the so
-called Nodal Severi varieties F(d\, \\nu). \n\nThe first basic questions
are: \n\n1) for which pairs is F(d\, \\nu) nonempty ? \n2) When is it irr
educible ?\n\nThe answer to 1) is known for d <= 6\, also the maximal numb
er of nodes \\mu (d) that a nodal surface in 3-space of degree d can have
is known\nonly for d <= 6.\n\nMaximizing nodal surfaces (those with \\mu
(d) nodes) are: the Cayley cubic\, the Kummer surfaces\, the Togliatti qui
ntics\, the Barth sextic.\n\nAn important chapter in Coding theory is the
theory of binary linear codes\, vector subspaces of a vector space (Z/2)^
n.\n\nI will recall basic notions and methods of coding theory (e.g. the M
cWilliams identities) and describe some codes related to quadratic forms.
\n\nNodal surfaces are related to coding theory via the first homology of
their smooth part: it is a binary code K\, which was used by Beauville\
nto show that\, for d=5 \, \\mu(d) = 31. Coding theory was crucial in orde
r to prove that \\mu(6) < = 65. \n\nOur main results concern the cases d =
4\,5\,6 (d=2\,3 being elementary). \n\nTHM 1. For d=4 the components of
F(4\, \\nu) and their incidence correspondence are determined by their ext
ended codes K’\,\nthese are all the shortenings of the first Reed Muller
code.\n\nWe extend this result to nodal K3 surfaces of all degrees\, this
sheds light on the case d=5.\n\nTHM 2. For d=5 F(5\, \\nu) is irreducib
le for \\nu = 31\, and the codes K occurring are classified\, up to a poss
ible exception.\nFor \\nu = 29\,30\,31 these surfaces are discriminants of
of the projection of a cubic hypersurface in 5-space. \n\nTHM 3. For d=6
and \\nu = 65 the codes K\, K’ are uniquely determined\, and can be d
escribed explicitly via\n the Hall graph\, attached to the group \\SigmaL
(2\, 25)\, and the gometry of the Barth sextic.\nEvery 65 nodal sextic occ
urs as discriminant of the projection of a cubic hypersurface in 6-space
with <=34 nodes.\n\n\nIrreducibility for d=6\, and 65 nodes\, is relate
d to the geometry of nodal cubic hypersurfaces in n-space\, and of the li
near subspaces contained in them.\n\nOne may ask whether\, in the case of
even dimension n\, the cubic hypersurface with maximal number of singulari
ties is\nprojectively equivalent to the Segre cubic s_1=s_3=0.\n\nFor theo
rem 2 I benefited of the cooperation of Sandro Verra\, for theorem 3 of
Yonghwa Cho\, Michael Kiermaier\, Sascha Kurz\nand the Linux Cluster of t
he Universitaet Bayreuth\, while \nDavide Frapporti and Stephen Coughlan
cooperated for the geometry of nodal cubic hypersurfaces.\n
LOCATION:https://researchseminars.org/talk/ColloquiumDiDipartimento/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Okounkov (Columbia University)
DTSTART;VALUE=DATE-TIME:20201203T150000Z
DTEND;VALUE=DATE-TIME:20201203T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171447Z
UID:ColloquiumDiDipartimento/4
DESCRIPTION:Title: Lie theory without groups\nby Andrei Okounkov (Columb
ia University) as part of Colloquium del dipartimento di Matematica - Roma
"Tor Vergata"\n\n\nAbstract\nLie theory\, which deals with smooth groups
of transformations\, is one of the cornerstones of mathematics and has gre
at importance for both theory and applications. It is also visibly limited
\, as the globe of Lie groups has been explored and inhabited. However\, i
n recent years\, some new geometric and algebraic structures have been rec
ognized as being as good as Lie groups in every respect\, including e.g. t
heir contribution to the supply of special functions. My goal in this talk
will be to explain where these new avenues of Lie theory lead.\n\nNote: T
his colloquium is part of the activity of the MIUR Department of Excellenc
e Project CUP E83C18000100006\n\nThe talk will be streamed via Microsoft T
eams. \n\nLink:\nhttps://teams.microsoft.com/l/meetup-join/19%3a2a9a822955
b54ca39f77f84130804b56%40thread.tacv2/1606245840781?context=%7b%22Tid%22%3
a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%229bfb10cf-6b03
-47dc-906c-d23eb368824c%22%7d\n
LOCATION:https://researchseminars.org/talk/ColloquiumDiDipartimento/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toshiyuki Kobayashi (The University of Tokyo)
DTSTART;VALUE=DATE-TIME:20210218T130000Z
DTEND;VALUE=DATE-TIME:20210218T140000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171447Z
UID:ColloquiumDiDipartimento/5
DESCRIPTION:Title: A foundation of group-theoretic analysis on manifolds
\nby Toshiyuki Kobayashi (The University of Tokyo) as part of Colloquium d
el dipartimento di Matematica - Roma "Tor Vergata"\n\n\nAbstract\nSymmetry
of geometry is inherited by symmetry of function spaces\, called the reg
ular representation. From this viewpoint\, the classical theory of expans
ions such as Fourier series or spherical harmonics may be interpreted as
"analysis and synthesis" of the regular representation.\n\n\nIn this tal
k\, we address the following fundamental questions about the regular repr
esentation on manifolds X acted algebraically by reductive Lie groups G s
uch as GL(n\,R).\n\nA. Does the group G "control well" the space of fu
nction on X?\nB. What can we say about "spectrum" for $L^2(X)$? \n\nWe
highlight "multiplicity" for A and "temperdness" for B\, and explain some
geometric ideas of the solution.\n\n**N.B.**: *this talk is part o
f the activity of the MIUR Excellence Department Project CUP E83C180001000
06*.\n
LOCATION:https://researchseminars.org/talk/ColloquiumDiDipartimento/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas J.R. Hughes (The University of Texas at Austin)
DTSTART;VALUE=DATE-TIME:20210426T150000Z
DTEND;VALUE=DATE-TIME:20210426T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171447Z
UID:ColloquiumDiDipartimento/6
DESCRIPTION:Title: Isogeometric Analysis: Origins\, Status\, Recent Progres
s and Structure Preserving Methods\nby Thomas J.R. Hughes (The Univers
ity of Texas at Austin) as part of Colloquium del dipartimento di Matemati
ca - Roma "Tor Vergata"\n\n\nAbstract\nThe vision of Isogeometric Analysis
(IGA) was first presented in a paper published October 1\, 2005 [1]. Sin
ce then it has become a focus of research within both the fields of Finite
Element Analysis (FEA) and Computer Aided Geometric Design (CAGD) and has
become a mainstream analysis methodology and provided a new paradigm for
geometric design [2-4]. The key concept utilized in the technical approac
h is the development of a new foundation for FEA\, based on rich geometric
descriptions originating in CAGD\, more tightly integrating design and an
alysis. Industrial applications and commercial software developments have
expanded recently. In this presentation\, I will describe the origins of
IGA\, its status\, recent progress\, areas of current activity\, and the
development of isogeometric structure preserving methods.\n\n\n**Key Word
s**: *Computational Mechanics\, Computer Aided Design\, Finite Element
Analysis\, Computer Aided Engineering*\n

\n\n\n**REFERENCES**\n<
br>\n[1] T.J.R. Hughes\, J.A. Cottrell and Y. Bazilevs\, Isogeometric Ana
lysis: CAD\, Finite Elements\, NURBS\, Exact Geometry and Mesh Refinement\
, Computer Methods in Applied Mechanics and Engineering\, 194\, (2005) 413
5-4195.\n

\n[2] J.A. Cottrell\, T.J.R. Hughes and Y. Bazilevs\, Isogeo
metric Analysis: Toward Integration of CAD and FEA\, Wiley\, Chichester\,
U.K.\, 2009.\n

\n[3] Special Issue on Isogeometric Analysis\, (eds. T.
J.R. Hughes\, J.T. Oden and M. Papadrakakis)\, Computer Methods in Applied
Mechanics and Engineering\, 284\, (1 February 2015)\, 1-1182.\n

\n[4]
Special Issue on Isogeometric Analysis: Progress and Challenges\, (eds. T
.J.R. Hughes\, J.T. Oden and M. Papadrakakis)\, Computer Methods in Applie
d Mechanics and Engineering\, 316\, (1 April 2017)\, 1-1270.

\n\n\n**N
B**:*This talk is part of the activity of the MIUR Excellence Departme
nt Project MATH@TOV CUP E83C18000100006*\n
LOCATION:https://researchseminars.org/talk/ColloquiumDiDipartimento/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Gigli (SISSA Trieste)
DTSTART;VALUE=DATE-TIME:20211216T150000Z
DTEND;VALUE=DATE-TIME:20211216T163000Z
DTSTAMP;VALUE=DATE-TIME:20240715T171447Z
UID:ColloquiumDiDipartimento/7
DESCRIPTION:Title: Differentiating in a non-differentiable environment\n
by Nicola Gigli (SISSA Trieste) as part of Colloquium del dipartimento di
Matematica - Roma "Tor Vergata"\n\n\nAbstract\nWe all know what the differ
ential of a smooth map from R to R is. By looking at coordinates and then
at charts\, we also know what it is the differential of a smooth map betw
een differentiable manifolds. With a little bit of work\, we can also def
ine a (weak) differential for Sobolev/BV maps in this setting (but the cas
e of manifold-valued maps presents challenges already at this level). In
this talk I will discuss how it is possible to differentiate maps between
spaces that have no underlying differentiable structure at all. The concep
ts of Sobolev/BV maps in this setting will also be discussed.

\n
\n **NB**:*This talk is part of the activity of the MIUR E
xcellence Department Project MATH@TOV CUP E83C18000100006*\n
\n
LOCATION:https://researchseminars.org/talk/ColloquiumDiDipartimento/7/
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