%PDF-1.3
1 0 obj
<< /Type /Catalog
/Outlines 2 0 R
/Pages 3 0 R >>
endobj
2 0 obj
<< /Type /Outlines /Count 0 >>
endobj
3 0 obj
<< /Type /Pages
/Kids [6 0 R
10 0 R
12 0 R
14 0 R
16 0 R
18 0 R
20 0 R
22 0 R
]
/Count 8
/Resources <<
/ProcSet 4 0 R
/Font <<
/F1 8 0 R
/F2 9 0 R
>>
>>
/MediaBox [0.000 0.000 612.000 792.000]
>>
endobj
4 0 obj
[/PDF /Text ]
endobj
5 0 obj
<<
/Creator (DOMPDF)
/CreationDate (D:20210410110124+00'00')
/ModDate (D:20210410110124+00'00')
/Title (SGCP Calendar)
>>
endobj
6 0 obj
<< /Type /Page
/Parent 3 0 R
/Contents 7 0 R
>>
endobj
7 0 obj
<<
/Length 3185 >>
stream
0.000 0.000 0.000 rg
BT 222.598 716.845 Td /F2 24.0 Tf [(Workshop Schedule)] TJ ET
BT 282.877 677.782 Td /F2 18.0 Tf [(Events for:)] TJ ET
BT 165.130 656.355 Td /F2 18.0 Tf [(Monday, March 8th - Friday, March 12th)] TJ ET
0.800 0.800 0.800 rg
83.134 615.256 484.969 19.632 re f
0.000 0.000 0.000 RG
0.75 w 0 J [ ] 0 d
84.259 616.381 482.719 17.382 re S
0.000 0.000 0.000 rg
BT 265.537 620.083 Td /F2 14.0 Tf [(Monday, March 8th)] TJ ET
BT 36.266 602.206 Td /F1 12.0 Tf [(9:00am)] TJ ET
BT 83.884 601.601 Td /F2 12.0 Tf [(Mitsuhiro Shishikura)] TJ ET
BT 83.884 572.230 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 572.230 Td /F1 12.0 Tf [(Reconstructing the germs of irrationally indifferent germs from renormalized sequence )] TJ ET
BT 83.884 543.545 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 543.545 Td /F1 12.0 Tf [(We discuss how to analyze the germs of irrationally indifferent germs of high type using )] TJ ET
BT 83.884 529.289 Td /F1 12.0 Tf [(the renormalized sequences. Key difference from unimodal maps or critical circle maps is that the )] TJ ET
BT 83.884 515.033 Td /F1 12.0 Tf [(domain of definitions of renormalizations overlap each other. We overcome this difficulty using the )] TJ ET
BT 83.884 500.777 Td /F1 12.0 Tf [(idea of dynamical charts and Decjoy odometer symbolic dynamics which governs the the )] TJ ET
BT 83.884 486.406 Td /F1 12.0 Tf [(combinatorics of pasting )] TJ ET
BT 36.266 443.326 Td /F1 12.0 Tf [(10:00am)] TJ ET
BT 83.884 442.721 Td /F2 12.0 Tf [(Pierre Berger)] TJ ET
BT 83.884 413.350 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 413.350 Td /F1 12.0 Tf [(gy in the Hénon family)] TJ ET
BT 83.884 399.065 Td /F1 12.0 Tf [(Abstract)] TJ ET
BT 124.540 399.065 Td /F2 12.0 Tf [(: )] TJ ET
BT 131.536 399.065 Td /F1 12.0 Tf [(We will present tools in bifurcation theory and a new theory on Hénon-like )] TJ ET
BT 83.884 384.809 Td /F1 12.0 Tf [(renormalization nearby homoclinic tangencies or chain of heteroclinic tangencies to deduce several )] TJ ET
BT 83.884 370.438 Td /F1 12.0 Tf [(new phenomena: )] TJ ET
BT 83.884 356.038 Td /F1 12.0 Tf [(- long renormalization strips in the space of Hénon-like families,)] TJ ET
BT 83.884 341.753 Td /F1 12.0 Tf [(- parametric embedding of composed quadratic families into the Hénon family \(Milnor swallow or )] TJ ET
BT 83.884 327.382 Td /F1 12.0 Tf [(Shrimp\) or nearby any non-degenerate 2-parameter homoclinic unfolding, )] TJ ET
BT 83.884 312.982 Td /F1 12.0 Tf [(- new examples of uniformly hyperbolic Hénon maps, with non trivial number of attracting cycles,)] TJ ET
BT 83.884 298.697 Td /F1 12.0 Tf [(- existence of wandering Fatou component among polynomial automorphisms of $\\mathbb R^2$, )] TJ ET
BT 83.884 284.326 Td /F1 12.0 Tf [(in a joint work with S. Biebler,)] TJ ET
BT 83.884 270.041 Td /F1 12.0 Tf [(- $Aut_d\(\\mathbb R^2\)$-universal family in the space of steady Euler flows \(Beltrami vector fields )] TJ ET
BT 83.884 255.670 Td /F1 12.0 Tf [(of $\\mathbb R^3$\), in a work in progress with A. Florio and D. Peralta-Salas.)] TJ ET
BT 36.266 212.590 Td /F1 12.0 Tf [(11:00am)] TJ ET
BT 83.884 211.985 Td /F2 12.0 Tf [(Natasha Goncharuk)] TJ ET
endstream
endobj
8 0 obj
<< /Type /Font
/Subtype /Type1
/Name /F1
/BaseFont /Times-Roman
/Encoding /WinAnsiEncoding
>>
endobj
9 0 obj
<< /Type /Font
/Subtype /Type1
/Name /F2
/BaseFont /Times-Bold
/Encoding /WinAnsiEncoding
>>
endobj
10 0 obj
<< /Type /Page
/Parent 3 0 R
/Contents 11 0 R
>>
endobj
11 0 obj
<<
/Length 4827 >>
stream
0.000 0.000 0.000 rg
0.000 0.000 0.000 RG
0.75 w 0 J [ ] 0 d
BT 83.884 732.214 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 732.214 Td /F1 12.0 Tf [(Bubbles and renormalization )] TJ ET
BT 83.884 703.529 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 703.529 Td /F1 12.0 Tf [(Take a cylinder of height $h$ and glue its boundaries via an analytic circle )] TJ ET
BT 83.884 689.273 Td /F1 12.0 Tf [(diffeomorphism $f$. The modulus of the resulting complex torus is called the complex rotation )] TJ ET
BT 83.884 675.017 Td /F1 12.0 Tf [(number of $f+ih$. Its limit as $h \\to 0$ is related \(and sometimes equal\) to the rotation number of )] TJ ET
BT 83.884 660.761 Td /F1 12.0 Tf [($f$. Add one more parameter: consider the map that takes $a+ih$ to the complex rotation number )] TJ ET
BT 83.884 646.505 Td /F1 12.0 Tf [(of $f+a+ih$. The limit values of this map as $h \\to 0$ form a fractal set ``bubbles''. Bubbles is a )] TJ ET
BT 83.884 632.249 Td /F1 12.0 Tf [(complex analogue to Arnold tongues. I will discuss the shapes and scaling of bubbles near rational )] TJ ET
BT 83.884 617.993 Td /F1 12.0 Tf [(and Diophantine rotation numbers, and the relation of these questions to renormalization operators )] TJ ET
BT 83.884 603.737 Td /F1 12.0 Tf [(in the space of conformal annuli maps. The talk is partly based on joint results with X.Buff and on )] TJ ET
BT 83.884 589.366 Td /F1 12.0 Tf [(joint results with M.Yampolsky. )] TJ ET
BT 36.266 546.286 Td /F1 12.0 Tf [(2:00pm)] TJ ET
BT 83.884 545.681 Td /F2 12.0 Tf [(Anatoly Dymarsky)] TJ ET
BT 83.884 516.310 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 516.310 Td /F1 12.0 Tf [(Scale invariance in quantum field theory )] TJ ET
BT 83.884 487.625 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 487.625 Td /F1 12.0 Tf [(In the context of unitary relativistic quantum field theory fixed points of the RG flow )] TJ ET
BT 83.884 473.369 Td /F1 12.0 Tf [(must exhibit scale invariance, yet all known examples are in fact conformal invariant. This )] TJ ET
BT 83.884 459.113 Td /F1 12.0 Tf [(enhancement of symmetry indicates a fundamental property of unitary relativistic QFTs, yet the )] TJ ET
BT 83.884 444.857 Td /F1 12.0 Tf [(one which is difficult to properly justify. This problem is only solved in two dimensions and partial )] TJ ET
BT 83.884 430.601 Td /F1 12.0 Tf [(progress has been achieved in four. In the talk I will review this problem, together with some recent )] TJ ET
BT 83.884 416.230 Td /F1 12.0 Tf [(progress, and outline possible directions for the future. )] TJ ET
BT 36.266 373.150 Td /F1 12.0 Tf [(3:00pm)] TJ ET
BT 83.884 372.545 Td /F2 12.0 Tf [(Svetlana Jitomirskaya)] TJ ET
BT 83.884 343.174 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 343.174 Td /F1 12.0 Tf [(On the critical almost Mathieu cocycle. )] TJ ET
BT 83.884 314.489 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 314.489 Td /F1 12.0 Tf [(The critical almost Mathieu cocycle is special in various ways. It represents a )] TJ ET
BT 83.884 300.233 Td /F1 12.0 Tf [(prototypical family of cocycles at the boundary between non-uniform hyperbolicity and )] TJ ET
BT 83.884 285.977 Td /F1 12.0 Tf [(reducibility. It is also the prototypical critical cocycle in the sense of Avila's global theory. Finally, )] TJ ET
BT 83.884 271.721 Td /F1 12.0 Tf [(it is the model behind the famous Hofstadter's butterfly and has been heavily studied in physics )] TJ ET
BT 83.884 257.465 Td /F1 12.0 Tf [(literature. Besides one Fields medal, it is linked to several Nobel prizes. We will present a complete )] TJ ET
BT 83.884 243.209 Td /F1 12.0 Tf [(proof of singular continuous spectrum for this family, for all phases, finishing a program with a )] TJ ET
BT 83.884 228.953 Td /F1 12.0 Tf [(long history, and based on a simple Fourier analysis and a new duality-type transform. We also )] TJ ET
BT 83.884 214.697 Td /F1 12.0 Tf [(present a result \(with I. Krasovsky\) that proves one half of the Thouless' one half conjecture from )] TJ ET
BT 83.884 200.441 Td /F1 12.0 Tf [(the early 80s: that Hausdorff dimension of the spectrum of the ubderlying Schrodinger operator \(the )] TJ ET
BT 83.884 186.185 Td /F1 12.0 Tf [(bifurcation set for the family of cocycles\) is bounded by 1/2 for all irrational frequencies. If time )] TJ ET
BT 83.884 171.929 Td /F1 12.0 Tf [(permits, we will also discuss recent progress towards the Thouless Catalan conjecture \(joint with I. )] TJ ET
BT 83.884 157.558 Td /F1 12.0 Tf [(Krasovsky and L. Konstantinov\). )] TJ ET
0.800 0.800 0.800 rg
83.134 106.396 484.969 19.632 re f
0.75 w 0 J [ ] 0 d
84.259 107.521 482.719 17.382 re S
0.000 0.000 0.000 rg
BT 265.145 111.223 Td /F2 14.0 Tf [(Tuesday, March 9th)] TJ ET
BT 36.266 93.346 Td /F1 12.0 Tf [(9:00am)] TJ ET
BT 83.884 92.741 Td /F2 12.0 Tf [(Davoud Cheraghi )] TJ ET
endstream
endobj
12 0 obj
<< /Type /Page
/Parent 3 0 R
/Contents 13 0 R
>>
endobj
13 0 obj
<<
/Length 4781 >>
stream
0.000 0.000 0.000 rg
0.000 0.000 0.000 RG
0.75 w 0 J [ ] 0 d
BT 83.884 732.214 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 732.214 Td /F1 12.0 Tf [(Complex Feigenbaum phenomena with degenerating geometries )] TJ ET
BT 83.884 703.529 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 703.529 Td /F1 12.0 Tf [(Renormalisation is a main focus of the theory of one-dimensional complex dynamics. It )] TJ ET
BT 83.884 689.273 Td /F1 12.0 Tf [(is connected to the central conjectures on the density of hyperbolicity and the local connectivity of )] TJ ET
BT 83.884 675.017 Td /F1 12.0 Tf [(the Mandelbrot set. For quadratic polynomials, there are two different types of renormalisations — )] TJ ET
BT 83.884 660.761 Td /F1 12.0 Tf [(primitive and satellite types. The primitive renormalisation has been successfully studied over the )] TJ ET
BT 83.884 646.505 Td /F1 12.0 Tf [(past few decades; the corresponding maps exhibit tame dynamical behaviour. The satellite type has )] TJ ET
BT 83.884 632.249 Td /F1 12.0 Tf [(a very different nature and remained mostly mysterious until recently. In this talk, we discuss the )] TJ ET
BT 83.884 617.993 Td /F1 12.0 Tf [(wide range of possibilities for the dynamics in presence of infinitely many satellite renormalisation )] TJ ET
BT 83.884 603.622 Td /F1 12.0 Tf [(structures. )] TJ ET
BT 36.266 560.542 Td /F1 12.0 Tf [(10:00am)] TJ ET
BT 83.884 559.937 Td /F2 12.0 Tf [(Theodore D Drivas)] TJ ET
BT 83.884 530.566 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 530.566 Td /F1 12.0 Tf [(Spontaneously stochastic solutions in dynamical systems with singularities )] TJ ET
BT 83.884 501.881 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 501.881 Td /F1 12.0 Tf [(We consider a class of dynamical systems described by ordinary differential equations )] TJ ET
BT 83.884 487.625 Td /F1 12.0 Tf [(with an isolated singularity, where the singularity is characterized by the lack of Lipschitz )] TJ ET
BT 83.884 473.369 Td /F1 12.0 Tf [(continuity. Singularities are common in applications both for ODEs \(e.g., particle collisions\) and )] TJ ET
BT 83.884 459.113 Td /F1 12.0 Tf [(PDEs \(e.g., finite-time blowup in fluid models\). The fundamental obstacle is that solutions cannot )] TJ ET
BT 83.884 444.857 Td /F1 12.0 Tf [(be continued past the singularity uniquely: typically, there are infinitely many solutions. The )] TJ ET
BT 83.884 430.601 Td /F1 12.0 Tf [(conventional way to proceed is to define a regularization limit, such as vanishing viscosity or noise. )] TJ ET
BT 83.884 416.345 Td /F1 12.0 Tf [(It turns out that there are structurally stable situations when such a limit is not sensitive to a )] TJ ET
BT 83.884 402.089 Td /F1 12.0 Tf [(particular form of regularization. This is explained by the analysis of attractors for the rescaled )] TJ ET
BT 83.884 387.833 Td /F1 12.0 Tf [(\(non-singular\) dynamical system and their ergodic properties. What is even more surprising is that )] TJ ET
BT 83.884 373.577 Td /F1 12.0 Tf [(solutions in this limit may become probabilistic \(spontaneously stochastic\) with the unique )] TJ ET
BT 83.884 359.321 Td /F1 12.0 Tf [(probability measure past the singularity. We will present rigorous results and discuss applications )] TJ ET
BT 83.884 345.065 Td /F1 12.0 Tf [(of this phenomenon. This is joint work with Alexei A. Mailybaev \(IMPA, Rio de Janeiro\) and )] TJ ET
BT 83.884 330.694 Td /F1 12.0 Tf [(Artem Raibekas \(UFF, Rio de Janeiro\). )] TJ ET
BT 36.266 287.614 Td /F1 12.0 Tf [(11:00am)] TJ ET
BT 83.884 287.009 Td /F2 12.0 Tf [(Charles Tresser)] TJ ET
BT 83.884 257.638 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 257.638 Td /F1 12.0 Tf [(RG: the hopes of K. Wilson about the ubiquity of RG: naivety or pure great vision? )] TJ ET
BT 36.266 214.558 Td /F1 12.0 Tf [(1:00pm)] TJ ET
BT 83.884 213.953 Td /F2 12.0 Tf [(Alexander Polyakov)] TJ ET
BT 83.884 184.582 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 184.582 Td /F1 12.0 Tf [(In praise of quantum field theory )] TJ ET
BT 83.884 155.897 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 155.897 Td /F1 12.0 Tf [(Quantum field theory provides a universal language for very different areas of physics. I )] TJ ET
BT 83.884 141.641 Td /F1 12.0 Tf [(will try to demonstrate this by briefly discussing some funda-mental problems, both solved and )] TJ ET
BT 83.884 127.385 Td /F1 12.0 Tf [(unsolved.cThe problems will include \(if time permits\) critical phenomena and conformal bootstrap, )] TJ ET
BT 83.884 113.129 Td /F1 12.0 Tf [(quark confine-ment and gauge/string duality, cosmological con-stant and turbulence, and may be )] TJ ET
BT 83.884 98.758 Td /F1 12.0 Tf [(more. )] TJ ET
BT 36.266 55.678 Td /F1 12.0 Tf [(2:15pm)] TJ ET
BT 83.884 55.073 Td /F2 12.0 Tf [(Pavel Bleher )] TJ ET
endstream
endobj
14 0 obj
<< /Type /Page
/Parent 3 0 R
/Contents 15 0 R
>>
endobj
15 0 obj
<<
/Length 4932 >>
stream
0.000 0.000 0.000 rg
0.000 0.000 0.000 RG
0.75 w 0 J [ ] 0 d
BT 83.884 732.329 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 732.329 Td /F1 12.0 Tf [(A Thouless-Like Effect in the Dyson Hierarchical Model with Continuous Symmetry )] TJ ET
BT 83.884 718.073 Td /F1 12.0 Tf [(Abstract. We study Dyson’s vector valued hierarchical models with continuous symme- try. We )] TJ ET
BT 83.884 703.817 Td /F1 12.0 Tf [(prove a conjecture of Dyson which states a necessary and sufficient condition of the existence of a )] TJ ET
BT 83.884 689.561 Td /F1 12.0 Tf [(phase transition in the models under consideration. We also prove another Dyson’s conjecture that )] TJ ET
BT 83.884 675.305 Td /F1 12.0 Tf [(in the presence of the phase transition the spontaneous magnetization vanishes at the critical point, )] TJ ET
BT 83.884 661.049 Td /F1 12.0 Tf [(i.e., there is no Thouless’ effect. On the other hand, we prove that the distribution of the normalized )] TJ ET
BT 83.884 646.793 Td /F1 12.0 Tf [(mean spin at the critical temperature Tc with free boundary conditions tends to a uniform )] TJ ET
BT 83.884 632.537 Td /F1 12.0 Tf [(distribution on the unit sphere as the volume tends to infinity, a phenomenon which resembles the )] TJ ET
BT 83.884 618.281 Td /F1 12.0 Tf [(Thouless effect. We prove that the limit distribution of the normalized average spin is Gaussian for )] TJ ET
BT 83.884 604.025 Td /F1 12.0 Tf [(T > Tc, and it is non-Gaussian for T ? Tc. We also show that the density of the limiting radial )] TJ ET
BT 83.884 589.769 Td /F1 12.0 Tf [(distribution for T ? Tc is a nice analytic function which can be found as a unique solution of a )] TJ ET
BT 83.884 575.513 Td /F1 12.0 Tf [(nonlinear fixed point renormalization group equation. Finally, we determine various critical )] TJ ET
BT 83.884 561.257 Td /F1 12.0 Tf [(asymptotics and show that the divergence of the correlation length and magnetic susceptibility are )] TJ ET
BT 83.884 546.886 Td /F1 12.0 Tf [(super-polynomial as T ? Tc. This is a joint work with P ?eter Major, Budapest, Hungary. )] TJ ET
0.800 0.800 0.800 rg
83.134 495.724 484.969 19.632 re f
0.75 w 0 J [ ] 0 d
84.259 496.849 482.719 17.382 re S
0.000 0.000 0.000 rg
BT 252.314 500.551 Td /F2 14.0 Tf [(Wednesday, March 10th)] TJ ET
BT 36.266 482.674 Td /F1 12.0 Tf [(9:00am)] TJ ET
BT 83.884 482.069 Td /F2 12.0 Tf [(Raphael Krikorian)] TJ ET
BT 83.884 452.698 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 452.698 Td /F1 12.0 Tf [(On the accumulation of non-split separtrices by invariant circles )] TJ ET
BT 83.884 424.013 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 424.013 Td /F1 12.0 Tf [( A theorem by M.R. Herman,``Herman's last geometric theorem'', asserts that if a smooth )] TJ ET
BT 83.884 409.757 Td /F1 12.0 Tf [(orientation and area preserving diffeomorphism $f$ of the 2-plane $\\R^2$ \(or the 2-cylinder )] TJ ET
BT 83.884 395.501 Td /F1 12.0 Tf [($\\R/\\Z\\times\\R$\) admits a KAM curve $C$ \(a smooth invariant curve on which the dynamics of )] TJ ET
BT 83.884 381.245 Td /F1 12.0 Tf [($f$ is conjugated to a Diophantine translation\) then $C$ is accumulated by other KAM curves, the )] TJ ET
BT 83.884 366.989 Td /F1 12.0 Tf [(union of which covers a set of positive 2-dimensional Lebesgue measure in any neighborhood of )] TJ ET
BT 83.884 352.733 Td /F1 12.0 Tf [($C$. In this talk we shall investigate whether such a phenomenon holds if, instead of being a KAM )] TJ ET
BT 83.884 338.477 Td /F1 12.0 Tf [(circle, the invariant set $C$ is a \(non-split\) separatrix of a hyperbolic fixed point of $f$. This )] TJ ET
BT 83.884 324.221 Td /F1 12.0 Tf [(analysis might be useful for understanding symplectic diffeomorphisms with zero entropy or in the )] TJ ET
BT 83.884 309.965 Td /F1 12.0 Tf [(search of a smooth twist map admitting an isolated irrational invariant curve bounding two Birkhoff )] TJ ET
BT 83.884 295.709 Td /F1 12.0 Tf [(instability regions. The renormalization paradigm is an important element in our approach. This is a )] TJ ET
BT 83.884 281.338 Td /F1 12.0 Tf [(joint work with Anatole Katok. )] TJ ET
BT 36.266 238.258 Td /F1 12.0 Tf [(10:00am)] TJ ET
BT 83.884 237.653 Td /F2 12.0 Tf [(Michael Yampolsky)] TJ ET
BT 83.884 208.282 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 208.282 Td /F1 12.0 Tf [(Renormalization convergence and rigidity of multicritical circle maps )] TJ ET
BT 83.884 179.597 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 179.597 Td /F1 12.0 Tf [(In a joint work with I. Gorbovickis we prove geometric convergence of renormalizations )] TJ ET
BT 83.884 165.341 Td /F1 12.0 Tf [(for C^3-smooth multicritical circle maps with rotation numbers of bounded type. From this, we )] TJ ET
BT 83.884 150.970 Td /F1 12.0 Tf [(obtain a C^{1+\\alpha} rigidity theorem for such maps. )] TJ ET
BT 36.266 107.890 Td /F1 12.0 Tf [(11:00am)] TJ ET
BT 83.884 107.285 Td /F2 12.0 Tf [(Selim Ghazouani )] TJ ET
endstream
endobj
16 0 obj
<< /Type /Page
/Parent 3 0 R
/Contents 17 0 R
>>
endobj
17 0 obj
<<
/Length 4359 >>
stream
0.000 0.000 0.000 rg
0.000 0.000 0.000 RG
0.75 w 0 J [ ] 0 d
BT 83.884 732.214 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 732.214 Td /F1 12.0 Tf [(Renormalisation of generalised interval exchange maps \(and foliations on surfaces\) )] TJ ET
BT 83.884 703.529 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 703.529 Td /F1 12.0 Tf [(Generalised interval exchange transformations \(GIETs\) are one-dimensional dynamical )] TJ ET
BT 83.884 689.273 Td /F1 12.0 Tf [(systems which naturally arise as first-return maps of flows/foliations on surfaces. Building upon )] TJ ET
BT 83.884 675.017 Td /F1 12.0 Tf [(work of Forni, Marmi-Moussa-Yoccoz and Khanin, I will attempt to draw a conjectural picture of a )] TJ ET
BT 83.884 660.761 Td /F1 12.0 Tf [(renormalisation theory that would give a satisfactory account of rigidity and geometric properties of )] TJ ET
BT 83.884 646.505 Td /F1 12.0 Tf [(GIETs. If time permits, I will try to highlight the important role that Lorentzian geometry should )] TJ ET
BT 83.884 632.134 Td /F1 12.0 Tf [(play in the development of such a theory. )] TJ ET
0.800 0.800 0.800 rg
83.134 580.972 484.969 19.632 re f
0.75 w 0 J [ ] 0 d
84.259 582.097 482.719 17.382 re S
0.000 0.000 0.000 rg
BT 257.753 585.799 Td /F2 14.0 Tf [(Thursday, March 11th)] TJ ET
BT 36.266 567.922 Td /F1 12.0 Tf [(9:00am)] TJ ET
BT 83.884 567.317 Td /F2 12.0 Tf [(Sebastian Van Strien)] TJ ET
BT 83.884 537.946 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 537.946 Td /F1 12.0 Tf [( Conjugacy classes of real analytic maps )] TJ ET
BT 83.884 509.261 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 509.261 Td /F1 12.0 Tf [(Avila-Lyubich-de Melo proved that the topological conjugacy classes of unimodal real-)] TJ ET
BT 83.884 495.005 Td /F1 12.0 Tf [(analytic maps are complex analytic manifolds, which laminate a neighbourhood of any such )] TJ ET
BT 83.884 480.749 Td /F1 12.0 Tf [(mapping without a neutral cycle. Their proof that the manifolds are complex analytic crucially )] TJ ET
BT 83.884 466.493 Td /F1 12.0 Tf [(depends on the fact that these are codimension-one in the space of unimodal mappings. In joint )] TJ ET
BT 83.884 452.237 Td /F1 12.0 Tf [(work with Trevor Clark, we show how to construct a “pruned polynomial-like mapping" associated )] TJ ET
BT 83.884 437.981 Td /F1 12.0 Tf [(to a real mapping. This gives a new complex extension of a real-analytic mapping. The additional )] TJ ET
BT 83.884 423.725 Td /F1 12.0 Tf [(structure provided by this extension, makes it possible to generalize this result of Avila-Lyubich-de )] TJ ET
BT 83.884 409.469 Td /F1 12.0 Tf [(Melo to interval mappings with several critical points. Thus we show that the conjugacy classes are )] TJ ET
BT 83.884 395.213 Td /F1 12.0 Tf [(complex analytic manifolds whose codimension is determined by the number of critical points. )] TJ ET
BT 83.884 380.957 Td /F1 12.0 Tf [(This result allows us to show density of real-hyperbolicity in families of real transcendental maps )] TJ ET
BT 83.884 366.701 Td /F1 12.0 Tf [(\(such as trigonometric polynomials\), even if the critical points of these maps are non-real. This )] TJ ET
BT 83.884 352.330 Td /F1 12.0 Tf [(generalises joint results with Lasse Rempe, and answers a question by Welington de Melo. )] TJ ET
BT 36.266 309.250 Td /F1 12.0 Tf [(10:00am)] TJ ET
BT 83.884 308.645 Td /F2 12.0 Tf [(Dzmitry Dudko )] TJ ET
BT 83.884 279.274 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 279.274 Td /F1 12.0 Tf [(Near-neutral renormalization in Complex Dynamics )] TJ ET
BT 83.884 250.589 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 250.589 Td /F1 12.0 Tf [(We will give an overview of near-neutral renormalization theories for quadratic )] TJ ET
BT 83.884 236.333 Td /F1 12.0 Tf [(polynomials and discuss how these theories relate to the renormalization of circle maps and to the )] TJ ET
BT 83.884 222.077 Td /F1 12.0 Tf [(problem of local connectivity of the Mandelbrot set. We will then discuss uniform a priori bounds )] TJ ET
BT 83.884 207.821 Td /F1 12.0 Tf [(for neutral polynomials that control how Siegel quasidisks degenerate when the rotation number )] TJ ET
BT 83.884 193.450 Td /F1 12.0 Tf [(becomes unbounded. Joint work with Misha Lyubich. )] TJ ET
BT 36.266 150.370 Td /F1 12.0 Tf [(11:00am)] TJ ET
BT 83.884 149.765 Td /F2 12.0 Tf [(Gregory Falkovich)] TJ ET
endstream
endobj
18 0 obj
<< /Type /Page
/Parent 3 0 R
/Contents 19 0 R
>>
endobj
19 0 obj
<<
/Length 3045 >>
stream
0.000 0.000 0.000 rg
0.000 0.000 0.000 RG
0.75 w 0 J [ ] 0 d
BT 83.884 732.214 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 732.214 Td /F1 12.0 Tf [(Fibonacci turbulence )] TJ ET
BT 83.884 703.529 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 703.529 Td /F1 12.0 Tf [(Never is the difference between thermal equilibrium and turbulence so dramatic, as )] TJ ET
BT 83.884 689.273 Td /F1 12.0 Tf [(when a quadratic invariant makes the equilibrium statistics exactly Gaussian with independently )] TJ ET
BT 83.884 675.017 Td /F1 12.0 Tf [(fluctuating modes. That happens in two very different yet deeply connected classes of systems: )] TJ ET
BT 83.884 660.761 Td /F1 12.0 Tf [(incompressible hydrodynamics and resonantly interacting waves. I shall describe an information-)] TJ ET
BT 83.884 646.505 Td /F1 12.0 Tf [(theoretic analysis of turbulence in such strongly interacting systems. We introduce a beautifully )] TJ ET
BT 83.884 632.249 Td /F1 12.0 Tf [(simple yet rich family of discrete models with neighboring triplet interactions and show that it has )] TJ ET
BT 83.884 617.993 Td /F1 12.0 Tf [(families of quadratic conservation laws defined by the Fibonacci numbers. Depending on the single )] TJ ET
BT 83.884 603.737 Td /F1 12.0 Tf [(model parameter, three types of turbulence were found: single direct cascade, double cascade, and )] TJ ET
BT 83.884 589.481 Td /F1 12.0 Tf [(the first ever case of a single inverse cascade. We describe quantitatively how deviation from )] TJ ET
BT 83.884 575.225 Td /F1 12.0 Tf [(thermal equilibrium all the way to turbulent cascades makes statistics increasingly non-Gaussian )] TJ ET
BT 83.884 560.969 Td /F1 12.0 Tf [(and find the self-similar form of the one-mode probability distribution. We reveal where the )] TJ ET
BT 83.884 546.713 Td /F1 12.0 Tf [(information \(entropy deficit\) is encoded and disentangle the communication channels between )] TJ ET
BT 83.884 532.457 Td /F1 12.0 Tf [(modes, as quantified by the mutual information in pairs and the interaction information inside )] TJ ET
BT 83.884 518.086 Td /F1 12.0 Tf [(triplets. )] TJ ET
BT 36.266 475.006 Td /F1 12.0 Tf [(4:00pm)] TJ ET
BT 83.884 474.401 Td /F2 12.0 Tf [(Coffee/discussion Break)] TJ ET
BT 36.266 454.750 Td /F1 12.0 Tf [(4:30pm)] TJ ET
BT 83.884 454.145 Td /F2 12.0 Tf [(Curtis McMullen, Math Colloquium)] TJ ET
BT 83.884 424.774 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 424.774 Td /F1 12.0 Tf [(Billiards and the arithmetic of non-arithmetic groups )] TJ ET
0.800 0.800 0.800 rg
83.134 373.612 484.969 19.632 re f
0.75 w 0 J [ ] 0 d
84.259 374.737 482.719 17.382 re S
0.000 0.000 0.000 rg
BT 266.706 378.439 Td /F2 14.0 Tf [(Friday, March 12th)] TJ ET
BT 36.266 360.562 Td /F1 12.0 Tf [(9:00am)] TJ ET
BT 83.884 359.957 Td /F2 12.0 Tf [(\(CANCELLED\) Marco Martens)] TJ ET
BT 83.884 330.586 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 330.586 Td /F1 12.0 Tf [(TBA )] TJ ET
BT 36.266 287.506 Td /F1 12.0 Tf [(10:00am)] TJ ET
BT 83.884 286.901 Td /F2 12.0 Tf [(Daniel Smania)] TJ ET
endstream
endobj
20 0 obj
<< /Type /Page
/Parent 3 0 R
/Contents 21 0 R
>>
endobj
21 0 obj
<<
/Length 5010 >>
stream
0.000 0.000 0.000 rg
0.000 0.000 0.000 RG
0.75 w 0 J [ ] 0 d
BT 83.884 732.214 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 732.214 Td /F1 12.0 Tf [(Infinitesimal deformations of one-dimensional maps )] TJ ET
BT 83.884 703.529 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 703.529 Td /F1 12.0 Tf [(Perhaps one of the main features of one-dimensional dynamics \(either real or complex\) )] TJ ET
BT 83.884 689.273 Td /F1 12.0 Tf [(is that the theory of deformations is rich. By this we mean that the topological classes of such maps )] TJ ET
BT 83.884 675.017 Td /F1 12.0 Tf [(often are infinite dimensional manifolds, but with finite codimension. Moreover for smooth )] TJ ET
BT 83.884 660.761 Td /F1 12.0 Tf [(families of maps inside a given topological class the associated family of conjugacies also moves )] TJ ET
BT 83.884 646.505 Td /F1 12.0 Tf [(on a smooth way. The derivative of this family of conjugacies with respect to the parameter is )] TJ ET
BT 83.884 632.249 Td /F1 12.0 Tf [(called an infinitesimal deformation. There are various applications in the study of renormalisation )] TJ ET
BT 83.884 617.993 Td /F1 12.0 Tf [(theory and linear response theory. The theory of holomorphic motions and its uses in complex )] TJ ET
BT 83.884 603.737 Td /F1 12.0 Tf [(dynamics is one the most famous incarnations of this phenomena. Lyubich used infinitesimal )] TJ ET
BT 83.884 589.481 Td /F1 12.0 Tf [(deformation in a crucial way to study the quadratic-like maps and renormalization theory on this )] TJ ET
BT 83.884 575.225 Td /F1 12.0 Tf [(setting, as well as Avila, Lyubich and de Melo in the study of generic behaviour of real-analytic )] TJ ET
BT 83.884 560.969 Td /F1 12.0 Tf [(unimodal maps. For real maps on the interval this phenomena also occurs, but our current )] TJ ET
BT 83.884 546.713 Td /F1 12.0 Tf [(understanding is far behind the complex setting. We will discuss the recents developments obtained )] TJ ET
BT 83.884 532.342 Td /F1 12.0 Tf [(in joint work with several collaborators: Viviane Baladi, Amanda de Lima and Clodoaldo Ragazzo. )] TJ ET
BT 36.266 489.262 Td /F1 12.0 Tf [(11:00am)] TJ ET
BT 83.884 488.657 Td /F2 12.0 Tf [(Igor Klebanov)] TJ ET
BT 83.884 459.286 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 459.286 Td /F1 12.0 Tf [(Confining or Not? )] TJ ET
BT 83.884 430.601 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 430.601 Td /F1 12.0 Tf [(The problem of Color Confinement in Yang-Mills theory is one of the deepest problems )] TJ ET
BT 83.884 416.345 Td /F1 12.0 Tf [(in theoretical physics. There is convincing numerical evidence from Lattice Gauge Theory, yet the )] TJ ET
BT 83.884 402.089 Td /F1 12.0 Tf [(proof of Confinement in Asymptotically Free theories has not been found. I will briefly introduce )] TJ ET
BT 83.884 387.833 Td /F1 12.0 Tf [(the Confinement problem and review some results on large N theories using the gauge/gravity )] TJ ET
BT 83.884 373.577 Td /F1 12.0 Tf [(duality. I will then discuss two-dimensional SU\(N\) theory coupled to an adjoint Majorana fermion. )] TJ ET
BT 83.884 359.321 Td /F1 12.0 Tf [(I will show that, when the adjoint mass is sent to zero, the spectrum retains a mass gap but the )] TJ ET
BT 83.884 345.065 Td /F1 12.0 Tf [(confinement disappears. Using the Discretized Light-Cone Quantization, I will discuss the )] TJ ET
BT 83.884 330.809 Td /F1 12.0 Tf [(spectrum of color singlet states and exhibit certain threshold states. Similar threshold states are also )] TJ ET
BT 83.884 316.553 Td /F1 12.0 Tf [(present in a model with a massless adjoint and a massive fundamental fermion. They provide new )] TJ ET
BT 83.884 302.297 Td /F1 12.0 Tf [(evidence for the lack of confinement. When the adjoint mass is turned on, the theory becomes )] TJ ET
BT 83.884 287.926 Td /F1 12.0 Tf [(confining, and the spectrum of bound states becomes discrete. )] TJ ET
BT 36.266 244.846 Td /F1 12.0 Tf [(1:30pm)] TJ ET
BT 83.884 244.241 Td /F2 12.0 Tf [(Giovanni Forni)] TJ ET
BT 83.884 214.870 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 214.870 Td /F1 12.0 Tf [( Ergodic properties of Billiards in Polygons, Renormalization and Hodge theory )] TJ ET
BT 83.884 186.185 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 186.185 Td /F1 12.0 Tf [(We survey old and new results on the ergodic theory of rational and non-rational )] TJ ET
BT 83.884 171.929 Td /F1 12.0 Tf [(billiards in polygons from the perspective of renormalization methods based on the so-called )] TJ ET
BT 83.884 157.673 Td /F1 12.0 Tf [(Teichmueller geodesic flow and related cocycles \(Kontsevich--Zorich, twisted\). We emphasize the )] TJ ET
BT 83.884 143.417 Td /F1 12.0 Tf [(role of Hodge theory in the analysis \(just started in the case of the twisted cocycle\) of their )] TJ ET
BT 83.884 129.046 Td /F1 12.0 Tf [(Lyapunov structure, which lies at the core of most of the results we will present. )] TJ ET
BT 36.266 85.966 Td /F1 12.0 Tf [(2:30pm)] TJ ET
BT 83.884 85.361 Td /F2 12.0 Tf [(Paul Wiegmann )] TJ ET
endstream
endobj
22 0 obj
<< /Type /Page
/Parent 3 0 R
/Contents 23 0 R
>>
endobj
23 0 obj
<<
/Length 1357 >>
stream
0.000 0.000 0.000 rg
0.000 0.000 0.000 RG
0.75 w 0 J [ ] 0 d
BT 83.884 732.329 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 114.880 732.329 Td /F1 12.0 Tf [(Almost Mathieu equation and representation theory: does it help to understand singular )] TJ ET
BT 83.884 717.958 Td /F1 12.0 Tf [(continuous spectrum? )] TJ ET
BT 83.884 689.273 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 135.532 689.273 Td /F1 12.0 Tf [(Almost Mathieu equation is the case study of operators with singular continuous )] TJ ET
BT 83.884 675.017 Td /F1 12.0 Tf [(spectrum. Most of \(extended\) studies of the spectrum belongs to the domain of functional analysis. )] TJ ET
BT 83.884 660.761 Td /F1 12.0 Tf [(At the same time, incidentally or not, the problem of Almost Mathieu operator can be formulated in )] TJ ET
BT 83.884 646.505 Td /F1 12.0 Tf [(terms of the representation theory of the \(quantum\) group $SL_q\(2\)$: its spectrum can be seen as )] TJ ET
BT 83.884 632.249 Td /F1 12.0 Tf [(weights of $SL_q\(2\)$ cyclic representation and obeys certain algebraic equation often called the )] TJ ET
BT 83.884 617.993 Td /F1 12.0 Tf [(Bethe Ansatz. In the talk I review this \(not-so-recent\) developments and formulate the problem of )] TJ ET
BT 83.884 603.622 Td /F1 12.0 Tf [(quantitative description of the spectrum in terms of yet to be determine critical exponents. )] TJ ET
endstream
endobj
xref
0 24
0000000000 65535 f
0000000009 00000 n
0000000074 00000 n
0000000120 00000 n
0000000333 00000 n
0000000362 00000 n
0000000499 00000 n
0000000562 00000 n
0000003799 00000 n
0000003908 00000 n
0000004016 00000 n
0000004081 00000 n
0000008961 00000 n
0000009026 00000 n
0000013860 00000 n
0000013925 00000 n
0000018910 00000 n
0000018975 00000 n
0000023387 00000 n
0000023452 00000 n
0000026550 00000 n
0000026615 00000 n
0000031678 00000 n
0000031743 00000 n
trailer
<<
/Size 24
/Root 1 0 R
/Info 5 0 R
>>
startxref
33153
%%EOF