Variations on a Theme by Kepler (Colloquium Publications)

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Nikolai Rimsky Korsakov - Variations on a Theme by Glinka

First Online: 05 March This process is experimental and the keywords may be updated as the learning algorithm improves. Download to read the full article text. Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author s and source are credited. Google Scholar. Derbes, Reinventing the wheel: Hodographic solutions to the Kepler problems, Am. CrossRef Google Scholar. Goldstein, Classical Mechanics , Addison-Wesley, 2nd edition.

Goodstein and J. Guillemin and S. Monthly 90 6 , — Moser, Regularization of the Kepler problem and the averaging method on a manifold, Comm. Pure Appl. Newton, Principia Mathematica , New translation by I. We verify it under some simple natural assumptions.

Translation invariant valuations which are continuous in the Hausdorff metric play a special role in the theory and its applications to integral geometry. Theory of such valuations is an active topic in convexity. In recent years it was realized that the space of such valuations admits rich structures, in particular the multiplicative structure. The latter turned out to be useful in integral geometry. First I will explain some of the classical background and examples.

Then I will discuss more recent results mentioned above. I will describe this technique, and will report on recent advances on the question what sort of "chaos" is needed to this method to succeed. The talk is meant for a general audience, including people with little or no background in dynamical systems. Descents of permutations have been studied for more than a century.

This concept was vastly generalized, in particular to standard Young tableaux SYT. More recently, cyclic descents of permutations were introduced by Cellini and further studied by Dilks, Petersen and Stembridge. Looking for a corresponding concept for SYT, Rhoades found a very elegant solution for rectangular shapes.

In an attempt to extend the concept of cyclic descents, explicit combinatorial definitions for two-row and certain other shapes have been found, implying the Schur-positivity of various quasi-symmetric functions. In all cases, the cyclic descent set admits a cyclic group action and restricts to the usual descent set when the letter n is ignored.

This talk will report on the surprising resolution of this conjecture: Cyclic descent sets exist for nearly all skew shapes, with an interesting small set of exceptions. The proof applies non-negativity properties of Postnikov's toric Schur polynomials and a new combinatorial interpretation of certain Gromov-Witten invariants.

We shall also comment on issues of uniqueness. The sloshing problem is a Steklov type eigenvalue problem describing small oscillations of an ideal fluid. We will give an overview of some latest advances in the study of Steklov and sloshing spectral asymptotics, highlighting the effects arising from corners, which appear naturally in the context of sloshing. In particular, we will outline an approach towards proving the conjectures posed by Fox and Kuttler back in on the asymptotics of sloshing frequencies in two dimensions.

The talk is based on a joint work in progress with M. Levitin, L. Parnovski and D. Model categories, introduced by Quillen, provide a very general context in which it is possible to set up the basic machinery of homotopy theory. In particalar they enable to define derived functors, homotopy limits and colimits, cohomology theories and spectral sequences to catculate them. However, the structure of a model category is usually hard to verify, and in some interesating cases even impossible to define.

In this lecture I will define a much simpler notion then a model category, called a weak fibration category. By a theorem due to T. Schlank and myself, a weak fibration category gives rise in a natural way to a model category structure on its pro category, provided some technical assumptions are satisfied. This result can be used to construct new model structures in different mathematical fields, and thus to import the methods of homotopy theory to these situations.

Applications will be discussed with each example. The above encompasses joint work with Tomer M. We present a new approach joint with M. By use of measure rigidity results of Bourgain-Furman-Lindenstrauss-Mozes and Benoist-Quint for algebraic actions on homogeneous spaces, we prove that for every set E of positive density inside traceless square matrices with integer values, there exists positive k such that the set of characteristic polynomials of matrices in E - E contains ALL characteristic polynomials of traceless matrices divisible by k.

Its discrete version is related to the 2D pentagram map defined by R. Schwartz in We will also describe its generalizations, pentagram maps on polygons in any dimension and discuss their integrability properties. While the topic of geometric incidences has existed for several decades, in recent years it has been experiencing a renaissance due to the introduction of new polynomial methods. This progress involves a variety of new results and techniques, and also interactions with fields such as algebraic geometry and harmonic analysis.

Studying incidence problems often involves the uncovering of hidden structure and symmetries. In this talk we introduce and survey the topic of geometric incidences, focusing on the recent polynomial techniques and results some by the speaker. We will see how various algebraic and analysis tools can be used to solve such combinatorial problems. In my talk based on joint work with D. Hecke-Hopf algebras have some other applications, most spectacular of which is the construction of new infinite families of solutions to the quantum Yang-Baxter equation. The studied properties mainly include covering properties, measure- and category-theoretic properties, and local properties in topological spaces, especially functions spaces.

Often, the characterization of a mathematical property using selectionprinciple is a nontrivial task leading to new insights on the characterized property. Which other domains admit such a basis?

A conformally invariant variational problem for time-like curves - INSPIRE-HEP

Fuglede conjectured that these so-called "spectral domains" could be characterized geometrically by their possibility to tile the space by translations. I will survey the subject and then discuss some recent results, joint with Rachel Greenfeld, where we focus on the conjecture for convex polytopes.

We explore results of Ramsey theory also known as partition calculus and show how they apply to cardinals, ordinals, trees, and arbitrary partial orders, leading up to the main result which is a generalization to trees of the Balanced Baumgartner-Hajnal-Todorcevic Theorem. This is true for reductive groups and the problem is open for unipotent groups. This action is extended to a representation in the algebra K[m].

Abstract is attached. We consider the issue of generalized stochastic processes, indexed by an abstract set of indices. What should the minimal required conditions on the indexing collection be, to study some of the usual properties of these processes, such as in- crement stationarity, martingale and Markov properties or integration question? The already known examples of processes indexed by functions or metric spaces can be addressed by this way. We show how the set-indexed framework of Ivanoff-Merzbach allows to study these generalized processes.

Some generalized processes can be defined as an integral with respect to some measure on the indexing collection. The links with function-indexed processes could be discussed. This talk is based on works in collaboration with Ely Merzbach and Alexandre Richard. Recall that the real line is that unique separable, dense linear ordering with no endpoints in which every bounded set has a least upper bound. A linear order is said to be separable if it has a countable dense subset. It is ccc if every pairwise-disjoint family of open intervals is countable.

Amazingly enough, the resolution of this single problem led to many key discoveries in set theory. Also, consistent counterexamples to this problem play a prominent role in infinite combinatorics. In this talk, we shall tell the story of the Souslin problem, and report on an advance recently obtained after 40 years of waiting.

This is joint work with J. Hall, S. Corson started a systematic study of certain topological properties of the weak topology w of Banach spaces E. This line of research provided more general classes such as reflexive Banach spaces, Weakly Compactly Generated Banach spaces and the class of weakly K-analytic and weakly K-countably determined Banach spaces. On the other hand, various topological properties generalizing metrizability have been studied intensively by topologists and analysts.

This is a simple consequence of a theorem of Schluchtermann and Wheeler that an infinite-dimensional Banach space is never a k-space in the weak topology. The study of subgroup growth, i. We shall discuss the Chirikov standard map, an area-preserving map of the torus to itself in which quasi-periodic and chaotic dynamics are believed to coexist. We shall describe how the problem can be related to the spectral properties of a one-dimensional discrete Schroedinger operator, and present a recent result. We define refined tropical enumerative invariants counting plane tropical curves of a given degree and a given positive genus and having marked points on edges and at vertices.

This extends Block-Goettsche and Goettsche-Schroeter refined tropical invariants. As a consequence we obtain tropical complex descendant invariants and real broccoli invariants of positive genus. We consider both time series as well as spatial distributions in dimensions. We note that this can explain observations of apparent cycles in mammalian animal populations.

We consider models, as well, based on the Langevin equation of kinetic theory and the Smolouchowski relation that present circumstances where the apparent period can vary from and, for a special subclass of problems, to periods between 2 and 3. We present a simple model for many mammalian population cycles whose underlying phenomenological basis has strong biological implications.

We then employ directed graphs to explore nearest-neighbor relationships and isolate the character of spatial clustering in dimension. We then take the first moment of each of the clusters formed, and observed that they too form clusters. We observe the emergence of a hierarchy of clusters and the emergence of universal cluster numbers, analogous to branching ratios and, possibly, Feigenbaum numbers. These, in turn, are related to fractals as well as succularity and lacunarity, although the exact nature of this connection has not been identified.

Variations on a Theme by Kepler

Finally, we show how hierarchical clustering emerging from random distributions may help provide an explanation for observations of hierarchical clustering in cosmology via the virial theorem and simulation results relating to the gravitational stabilization in a self-similar way of very large self-gravitating ensembles. This discrete geometry problem was posed by Gowers in , and it is a special case of an open problem posed by Danzer in I will present two proofs that answers Gowers' question with a NO. The first approach is dynamical; we introduce a dynamical system and classify its minimal subsystems.

This classification in particular yields the negative answer to Gowers' question. The second proof is direct and it has nice applications in combinatorics. The talk will be accessible to a general audience. In , Arthur Cayley defined a correspondence between orthogonal matrices of determinant one and skew-symmetric matrices. This observation was a starting point of a long and yet unfinished story.

In the talk we will overview its highlights, with a focus on the achievements obtained during the past decade and some open problems. The first main result of the talk is the solution to the problem, posed by Borodin and Olshanski in , of the explicit description of the ergodic decomposition of infinite Pickrell measures. For different values of the parameter s, these measures are mutually singular. In the second part of the talk we will discuss absolute continuity and singularity of determinantal point processes.

The main result here is that determinantal point processes on Z induced by integrable kernels are indeed quasi-invariant under the action of the in nite symmetric group. The Radon-Nikodym derivative is found explicitly. A key example is the discrete sine-process of Borodin, Okounkov and Olshanski. This result has a continuous counterpart: namely, that determinantal point processes with integrable kernels on R, a class that includes processes arising in random matrix theory such as the sine-process, the process with the Bessel kernel or the Airy kernel, are quasi-invariant under the action of the group of di eomorphisms with compact support.

In Helmut Hofer introduced a bi-invariant metric on symplectomorphism groups which nowadays plays an important role in symplectic topology and Hamiltonian dynamics. I will review some old, new and yet unproved results in this direction. Although higher structures have been around for quite some time, they recently have come back into focus through renewed interest in higher categories.

There are several reasons for this. In geometry one is trying to interpret extended cobordism theories, where the higher structures are meant to mimic higher codimensions. An analogue in algebra is known to the 2-categorical level, the prime example being the 2-category of rings, bi-modules and bi-module morphisms. Beyond this there are many open questions of fundamental nature. The central problem is what type of coherence to require.

In physics higher structures naturally appear in two related fashions. The first is through the extended field theories and the second through field theories with defects. This is mathematically mimicked by cobordisms and defect lines and points abstractly interpreted as inclusions into higher dimensional objects. The "truncated" versions of higher structures can be assembled into infinity up to a homotopy everything version.

This is the setting of the influential program of Lurie which provides firm foundations to derived algebraic geometry, and, hopefully, to higher differential geometry which is not yet that well established. Geometric and physical points of view combine in the constructions of string topology and in the proofs of the cobordism hypothesis. The classical homotopy theory teaches us that this is the correct way to encode higher homotopies and homotopical algebra in general.

The complexity of higher dimensional structures and necessity to work with them efficiently has required reconsideration of the foundations of mathematics. A new theory called univalent foundations or homotopy type theory emerges in recent years which has a potential to become a common language for mathematicians working with higher categorical structures. We wish to include this theory as a supplement to our main topics, but also as a possible future direction of research.

The Cerny conjecture, concerned with the minimal length of a reset word in a finite automata, is considered one of the most longstanding open problem in the theory of finite automata. In the second part, we present our recent results, which shade a light on the question of why the conjecture is so hard to prove. Suppose a light source is placed in a polygonal hall of mirrors so light can bounce off the walls. Does every point in the room get illuminated? This elementary geometrical question was open from the s until Tokarsky found an example of a polygonal room in which there are two points which do not illuminate each other.

Resolving a conjecture of Hubert-Schmoll-Troubetzkoy, in joint work with Lelievre and Monteil we prove that if the angles between walls is rational, every point illuminates all but at most finitely many other points. The proof is based on recent work by Eskin, Mirzakhani and Mohammadi in the ergodic theory of the SL 2,R action on the moduli space of translation surfaces. The talk will serve as a gentle introduction to the amazing results of Eskin, Mirzakhani and Mohammadi. Non-Archimedean analytic geometry is an analog of complex analytic geometry over non-Archimedean e.

In the talk, I'll explain what non-Archimedean analytic spaces are, list basic facts about them, and tell about their applications. Hyperbolic groups can be defined through the geometry of Cayley graphs, viewed as geodesic metric spaces. One important feature of hyperbolic groups is the concept of boundary, which can be defined through the topological completion for an appropriate metric such as the visual metrics , and has the advantages of compactness.

However, this stronger claim does not necessarily hold for arbitrary hyperbolic groups. Cooperative interactions, their stability and evolution, provide an interesting context in which to study the interface between cellular and population levels of organization.

Such interactions also open the way for the discovery of new population dynamics mechanisms. We have studied a version of the public goods model relevant to microorganism populations actively extracting a growth resource from their environment. Cells can display one of two phenotypes — a productive phenotype that extracts the resources at a cost, and a non-productive phenotype that only consumes the same resource.

We analyze the continuous differential equation model as well as simulate stochastically the full dynamics. It is found that the two sub-populations, which cannot coexist in a well-mixed environment, develop spatio-temporal patterns that enable long-term coexistence in the shared environment. These patterns are solely fluctuation-driven, since the continuous system does not display Turing instability.

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The average stability of the coexistence patterns derives from a dynamic mechanism in which one sub-population holds the environmental resource close to an extinction transition of the other, causing it to constantly hover around its critical transition point, forming a mechanism reminiscent of selforganized criticality. Accordingly, power-law distributions and long-range correlations are found.

When a time scale separation occurs between two dynamic parameters is defined, a structurally unstable point emerges and any small perturbation of the dynamics with additive noise leads to an equilibrium distribution in which both species coexist in context of additive but not multiplicative noise.

For three quarters of a century Linear Programming LP was the main tool for solving resource allocation problems RAP - one of the main problem in economics. In L. Kantorovich and T. Linear Programming for resource allocation problems. When LP is used for RAP the prices for goods and the resource availability are given a priori and independent on the production output and prices for the resources. It often leads to solutions, which are not practical, because they contradict to the basic market law of supply and demand. The NE is a generalisation of Walras-Wald equilibrium, which is equivalent to J Nash equilibrium in n-person concave game.

NE eliminates the basic drawbacks of LP. Finding NE is equivalent to solving a variation inequality VI on the Cartesian product of the primal and dual non negative octants, projection on which is a very simple operation. For solving the VI we consider two methods: projected pseudo-gradient PPG and extra pseudo-gradient EPG , for which projection is the main operation at each step. We established convergence, proved global Q-linear rate and estimated complexity of both methods under various assumptions on the input data.

In many cases just a finite part of Taylor expansion is enough to determine f up to the change of coordinates. Alternatively, the deformations of f by terms of high enough orders are trivial. This phenomenon is called the finite determinacy. An immediate application is the algebraization: f has a polynomial representative.

More generally, for maps of smooth spaces the finite determinacy under various group-actions has been intensively studied for about 50 years by Mather, Tougeron, Arnol'd, Wall and many others. The game duration problem BLS have proved the remarkable result that whenever this game terminates, it always does so in the same number of moves, irrespective of gameplay! I will explain the background for this. They also gave an elegant upper bound on the number of moves. However, computer simulation reveals that the game actually ends in far fewer moves than the BLS bound in all examined cases.

The new results I will show a new approach to obtaining upper bounds on the game duration, based on a re nement of the classic BLS analysis together with a simple but potent new observation. The new bounds are always at least as good as the BLS bound and in some cases the improvement is dramatic. The proof technique involves a careful analysis of the pseudo-inverse of the graph's discrete Laplacian.

The wider context Time permitting, I will also discuss the appearance of chip ring and its very close relative, the sandpile model in diverse mathematical and scientific contexts. The Inverse Galois Problem, asking which groups can be realizable as Galois groups of fields, is a major problem in Galois theory. Minac and Tan conjectured that if G is the Galois group of a field, then G has vanishing triple Massey products to be defined in the lecture. In the talk I will give some general background on this new property and its relation to the inverse Galois problem via a work of Dwyer, and try to give a flavor of my proof of the Minac-Tan conjecture.

Ergodic theory studies actions of a group G by measure preserving transformations on a probability space. Usually the focus is on "essentially free" actions, namely actions for which almost all stabilizers are tirival. Classically the methods are analitic and combinatorial. Recently it becomes more and more clear that in the study of non essentially free actions - sophisticated group theoretic tools also come into the picture. I will try to demonstrate this by an array of recent results due to Bader-Lacreux-Duchnese, Tucker-Drob, as well as some joint papers with Abert and Virag and myself.

The subject of this talk is the analysis of pure point distributions that have a pure point spectrum. The purpose of this talk is to present an answer on a similar question in the case of algebraic operads. Namely, I will show that the generating series of a generic nonsymmetric operad is an algebraic function and the generating series of a generic symmetric operad is differentially algebraic. Despite the motivation coming from the operad theory, a substantial part of the talk will only deal with the avoidance problems for labeled rooted trees hence will be accessible to nonspecialists.

Indeed, social, biological and technological systems feature highly random and non-localized interaction patterns, which challenge the classical connection between structure, dimensionality and dynamics, and hence confront us with a potentially new class of dynamical behaviors. We find that while microscopically complex systems follow diverse rules of interaction, their macroscopic behavior condenses into a discrete set of dynamical universality classes. Relevant papers: Universality in network dynamics. Nature Physics 9, — doi Nature Biotechnology 31, — doi In some models, like internal DLA and rotor-router aggregation, the scaling limits are universal; in particular, starting from a point source yields a disk.

In the abelian sandpile, particles are added at the origin and whenever a site has four particles or more, the top four particles topple, with one going to each neighbor. Despite similarities to other models, for the sandpile, the intriguing pattern that arises is not circular and depends on the particular lattice. A scaling limit exists for the sandpile, as was recently shown by Pegden and Smart, but it is not universal and still mysterious.

This research has been greatly influenced by pictures of the relevant sets, which I will show in the talk. They suggest a connection to conformal mapping which has not been established yet. Talk based on joint works with Lionel Levine. The main focus will be on the group large sieve method which is a tool for estimating the density by investigating the finite quotients of the group.

We will describe applications of this method for linear groups as well as for mapping class groups. The theory of analytic quantum groups was developed in order to provide a framework for duality of general locally compact groups. In this talk we will motivate and introduce the definition of LCQGs, explain and exemplify how they are constructed and mention some of their applications. Afterwards, we shall describe a generalization of recent work on aspects of ergodic theory of semigroup actions on von Neumann algebras to the context of quantum semigroups.

These results give a Jacobs-de Leeuw-Glicksberg splitting at the von Neumann algebra level. This geometry problem is the focus of much activity these days and I will survey some results of my own and of others aimed at better understanding the rich energy landscape that emerges from the interplay between these two competing terms in the problem. We start with a simple fact: the fundamental solutions of the Laplacian in Rn can be continued as multi-valued. In fact, those results remain true for such operators with degree bigger than 4 , but the proofs are different due to the lack of natural geodesic distance associated to the operators.

Those results may be connected with D-module theory, and more precisely with regular holonomic D-Modules. Paul Cohen showed that the Continuum Hypothesis is independent of the usual axioms of set theory. As Cohen predicted, the method of forcing became very successful in establishing the independence of various statements from the usual axioms of set theory.

What Cohen never imagined, is that forcing would be found useful in proving theorems.

In this talk, we shall present a few results in combinatorics whose proof uses the method of forcing, including our recent resolution of the infinite weak Hedetniemi conjecture. One of many intractable questions is under what conditions one have the number of nodal domains to be unbounded as the eigenvalue goes to infinity.

The main difficulty in this problem is that it is known not to be a local property. The example I will consider concerns with eigenfunctions of the Laplace-Beltrami operator on compact hyperbolic surfaces. The distinctive property of such a setup is its Quantum Unique Ergodicity to be explained. I will discuss how this could be used in order to deduce strong bounds on eigenfunctions and how this forces the number of nodal domains to grow with the eigenvalue. A central question in the theory of random walks on groups is how symmetries of the underlying space gives rise to structure and rigidity of the random walks.

This answers a question of Vershik, Naor and Peres. In other examples, the speed exponent can fluctuate between any two values in this interval. We will then show how groups of automorphisms of rooted trees, related to automata groups , can then be constructed and analyzed to get the desired rate of escape. This is joint work with Balint Virag of the University of Toronto.

No previous knowledge of randopm walks, automaton groups or wreath products is assumed. Communication networks are vulnerable to natural disasters, such as earthquakes or floods, as well as to physical attacks, such as an Electromagnetic Pulse EMP attack.

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Such real-world events happen in specific geographical locations and disrupt specific parts of the network. Therefore, the geographical layout of the network determines the impact of such events on the network's connectivity. Thus, it is desirable to assess the vulnerability of geographical networks to such disasters. I will discuss several algorithms, based on mixed linear planning and computational geometry, to locate such vulnerabilities, and present some case studies on real networks.

For such groups one can define the k-1 -dimensional Dehn function, which measures the difficulty to fill k-1 -cycles by k-chains. The Riemann Zeta-Function is simple to define but utterly impossible to find all its zeros. Euler looked at it a century before Riemann to study the prime numbers and the value of the zeta function at the integers.

By , many far-reaching mysteries were uncovered. We shall describe them, as well as today's Conjectures of Langlands and Iwasawa which are built upon them. Skip to main content Skip to main Navigation. Search Form. Search this site:. Secondary Menu. Print Tell a Friend. Organizer s :. Margolis Stuart. Solomyak Boris. Usual Time:. Room in the Math Department. Lectures from past years:. Mathematics Colloquium RSS feed. Previous Lectures.

Title : L-functions, periods and quantization of representations. Abstract: I will discuss new analytic developments in the old paradigm in automorphic functions connecting L-functions to representation theory via the fundamental notion of a period. Dimitri Gourevitch, University of Valenciennes, France. Title : What is "quantum determinant"?

I plan to introduce the notion of QMAs and quantum analogs of some symmetric polynomials in these algebras. In particular, such "quantum symmetric elements" in Generalized Yangians will be exhibited. Also, I plan to discuss the role of these objects in Integrable Systems theory. Title : Logical properties of random graphs. Title : On some aspects of the coupon collector's problem.

Abstract: Suppose that a company distributes a commercial product and that each package contains a coupon. Title : Dynamically defined function graphs. Abstract: This talk is an overview on the dimension theory of some dynamically defined function graphs, like Takagi and Weierstrass function. Title : Large cardinals, substructures, and Chang's Conjecture. Abstract: One of the basic results in model theory is Lowenheim-Skolem. Title : Products of uncountable structures. Speaker: Gady Kozma, Weizmann Institute. Title : Cantor uniqueness along subsequences. Abstract: In Cantor proved that a trigonometric series which converges to zero everywhere must be trivial.

Speaker: Dmitry Novikov, Weizmann Institute. Title : Complex Cellular Structures. Abstract: Real semialgebraic sets admit so-called cellular decomposition, i. This is a joint work with Gal Binyamini. Speaker: Amos Nevo, the Technion. Title : New directions in entropy theory. Abstract: In recent years, the classical theory of entropy for a dynamical system has been revolutionized by the ground-breaking work of several researchers.

Pogorzelski Leipzig University. Yotam Smilansky, The Hebrew University. Title : Multiscale substitution schemes and Kakutani sequences of partitions. Abstract: Substitution schemes provide a classical method for constructing tilings of Euclidean space. Speaker: Gregory Soifer, Bar-Ilan. Title : Discreteness of deformations of co-compact discrete subgroups.

Speaker: Dr. Abstract: We describe several examples of tame subgroups of finitely presented groups and prove that the fundamental groups of certain finite graphs of groups are locally tame. Yuval Peres, Microsoft Research. Speaker: Prof. Title : Gravitational matching and allocation for uniform points on the sphere.

Abstract: Given n uniform points on the surface of a two-dimensional sphere, how can we partition the sphere fairly among them? Speaker: Sara Tukachinsky, Princeton University. Title : Counting holomorphic disks using bounding chains. Title : Interlocking Structures. Speaker: Tali Pinsky, Technion. Title : Complements of closed geodesics. Abstract: I will describe some nice connections between closed geodesics on surfaces, knot theory, continued fractions and hyperbolic three-manifolds.

Title : On semi-conjugate rational functions.

Book Variations On A Theme By Kepler Colloquium Publications

Title : Angles of Gaussian primes. Title : The Junta Method for Hypergraphs. In this talk we present a general approach to such problems, using a 'junta approximation method' that originates from analysis of Boolean functions. Joint work with Noam Lifshitz. Ron Peled, Tel-Aviv University. Title : The proper way to color a grid.

Jake Solomon, Hebrew University. Title : Singular Lagrangian intersections and the non-linear Cauchy-Riemann equation. Abstract: A classical result of Lojasiewicz says that a bounded gradient flow trajectory of a real analytic function converges to a unique limit. Victor Vinnikov Ben-Gurion University. Title : Free Noncommutative Function Theory.

Abstract: Noncommutative functions are graded functions between sets of square matrices of all sizes over two vector spaces that respect direct sums and similarities. Danny Neftin, Technion. Title : Ritt decompositions the known, unknown, and their applications. Gil Ariel, Bar-Ilan University. Abstract: Bacterial swarming is a collective mode of motion in which cells migrate rapidly over surfaces. Menachem Shlossberg, University of Udine. Title : Hereditarily minimal topological groups. We study hereditarily minimal groups.

The following theorem is one of our main results. Toller and W. Eliyahu Rips, Hebrew University. Title : Small cancellation for groups and rings. Victor Vinnikov, Ben-Gurion University. Title : Free noncommutative function theory. Title : Colorful coverings of polytopes -- the topological truth behind different colorful phenomena. Naomi Feldheim Weizmann Institute. Title : Gaussian stationary processes: a spectral perspective.

Mark Agranovsky. Title : On algebraically integrable bodies. Arnold proposed to generalize Newton's observation to higher dimensions and conjectured that all smooth bodies, with the exception of ellipsoids in odd-dimensional spaces, have an analogous property. The talk is devoted to the current status of the conjecture. Shmuel Weinberger, "University of Chicago. Speaker: "Prof. Shmuel Weinberger University of Chicago. Title : How can it be true? Abstract: Over 60 years ago, Borel, on the basis of theorems of Mostow, conjectured a topological rigidity statement that has become central to topology.

Title : How can it be true. Tahl Nowik. Abstract: Introductory lecture for Prof. Weinberger's lecture. Misha Bialy Tel Aviv University. Title : Around Birkhoff's conjecture for convex and other billiards. Abstract: Birkhoff's conjecture states that the only integrable billiards in the plane.

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I am going to give a survey of recent progress in this conjecture and to discuss. Title : On the subsemigroup complex of an aperiodic Brandt semigroup. Abstract: Taking as departure point an article by Cameron, Gadouleau, Mitchell and Peresse on maximal lengths of subsemigroup chains, we introduce the subsemigroup complex H S of a nite semigroup S as a boolean representable simplicial complex de fined through chains in the lattice of subsemi- groups of S. Title : Groups with Polynomial Identities. Abstract: Algebras with Polynomial Identities is a well developed theory with strong Israeli roots.

Title : Functoriality for the classical groups using the generalized doubling method. Speaker: Tobias Hatnick, The Technion. Title : Geometric group theory beyond groups. Abstract: In this talk I will first explain the basic ideology behind geometric group theory: How and to what extend can we understand finitely-generated groups as geometric objects? Speaker: Tobias Hartnick, The Technion. Mathematical developments arising from Hilbert 18th problem. Title : The fundamental group of an affine manifold. In J. Milnor stated the following question: Question: Does there exist a complete affinely flat manifold M such that the fundamental group of M contains a free group?

Title : First-order logic on the free group. Abstract: We will give an overview of questions one might ask about the first-order theory of free groups and related groups: how much information can first-order formulas convey about these groups or their elements, what algebraic interpretation can be given for model theoretic notions. Abstract: In recent decades it became clear that applications of Ergodic Theory are useful for the study of linear groups, remarkable examples being Mostow and Margulis Rigidity Theorems.

What began as a collection of ad-hoc methods is getting now the shape of an organized theory. In my talk I survey some old and new ideas and results in this direction. No prior knowledge of Ergodic Theory will be assumed.