It will start on thursday dec 3 with introductory lectures by laura demarco and mattias jonsson. Analysis of eigenvalues topology and torsion classes algebraic geometry 1 analysisofeigenvalues 2 topologyandtorsionclasses 3 algebraicgeometry akshay venkatesh iasstanford analysis and topology on arithmetic locally symmetric spaces. I let students know that what makes it an arithmetic sequence is that there is a constant difference between consecutive terms. Conference on the occasion of the 70 th birthday of lucien szpiro. The graduate center of the city university of new york. The study of arithmetic dynamics draws on ideas and techniques from both classical discrete dynamical systems and the theory of diophantine equations.
In number theory, an arithmetic, arithmetical, or numbertheoretic function is for most authors any function fn whose domain is the positive integers and whose range is a subset of the complex numbers. Room 420, research institute for mathematical sciences. Moduli spaces for dynamical systems with portraits. Current trends and open problems in arithmetic dynamics. Moduli spaces associated to dynamical systems the geometry of dynamical moduli spaces dynamical moduli spaces further topics dynatomic polynomials and dynamical modular curves canonical heights postcritically finite maps field of moduli and field of definition. In an arithmetic progression, the first number in the series is called the initial term. This operator performs the same functionality as the c pow function. Lecture notes on arithmetic dynamics arizona winter school. Galois theory of orbits in arithmetic dynamics, aim 22516. Dynamics, geometry, and the moduli space of riemann surfaces. The arithmetic of dynamical systems, springerverlag, gtm 241, 2007, theres also the following monograph that discusses dynamicalrelated moduli spaces from an algebraic and arithmetic viewpoint. Moduli spaces and arithmetic dynamics, crm monograph series 30, ams, 2012.
The authors goal is to provide an overview, with enough details and pointers to the existing literature, to give the reader an entry into this. Pdf an arithmeticalgebraic work space for the promotion of. This article provides links to functions of both classes. The algorithm performs a conflictdriven clause learning cdclstyle search for a feasible assignment, while using projection operators adapted from cylindrical algebraic decomposition to guide the search away from the conflicting states. It also includes some additional material that was referenced in the arithmetic of dynamical systems springerverlag gtm 241 and some miscellaneous ar. It is an expanded version of the notes for a series of lectures delivered at a workshop on moduli spaces and the arithmetic of dynamical systems at the bellairs research institute, barbados, in 2010. The space of rational selfmaps of pn 10 moduli spaces of semistable rational maps theorem. Arithmetic branching programs with memory stefanmengel. Arithmetic and algebra worksheets adventist circle. Topology festival cornell university, ithaca, new york, may 2020. More precisely, one studies the space of isomorphism classes of varieties having a speci ed structure, i.
The arithmetic of dynamical systems brown university. This monograph studies moduli problems associated to algebraic dynamical systems. Lecture notes on arithmetic dynamics arizona winter school march. This lesson aims to introduce arithmetic sequences and geometric sequences to secondary school students. An arithmeticalgebraic work space for the promotion of arithmetic and algebraic thinking. The aim of this talk is to describe some of the moduli spaces that come up in dynamics, and to see how. Complex dynamics, families and friends, ak peters, 2009. Moduli spaces and arithmetic dynamics crm monograph. There is a larger class of numbertheoretic functions that do not fit the above definition, for example, the primecounting functions. The verilog2001 standard adds five enhancements to provide greater signed arithmetic capability. The authors goal is to provide an overview, with enough details and pointers to the existing literature.
This identity is nontrivial and relies on the equivalence of each approach to kdv equations. Extend the operation to the powerset pm of m and 2. The fth term of a geometric sequence of positive numbers is 11 and the eleventh term is 5. Towards an arithmetic for partial computable functionals basil a. The research part of the workshop will start on friday dec 4. To find a rule for s n, you can write s n in two different ways and add the results. Martin hofmann january 19, 2000 abstract a classical quanti. Classically, discrete dynamics refers to the study of the iteration of selfmaps of the complex plane or real line. Topology and arithmetic of resultants, i benson farb and jesse wolfson abstract. Ninth grade lesson exploring an arithmetic sequence dots. We show that two natural approaches to quantum gravity coincide. In arithmetic geometry, rather than studying one variety, it is fruitful to look at the space of all varieties. The authors goal is to provide an overview, with enough details and pointers to the existing literature, to give the reader an entry into this exciting area of current research. Arithmetic dynamics has, for the most part, been focussed on the iteration of endomorphisms of a variety.
Arithmetic operations in interval spaces springerlink. The galois theory of orbits in arithmetic dynamics edited by org. If m is an ordered algebraic structure every operation can be extended to intervals over m by the following two steps. Arithmetic dynamics is a field that amalgamates two areas of mathematics, dynamical systems and number theory. For example, the sequence 2, 4, 6, 8, 2, 4, 6, 8, \dots 2, 4, 6, 8, is an arithmetic sequence with the common difference 2 2 2. Moduli spaces for dynamical systems brown university. Mathematics arithmetic geometry arithmetic dynamics conference. Model theory and arithmetic dynamics, fields institute 51716. We consider the interplay of point counts, singular cohomology, etale cohomology, eigenvalues of the frobenius and the grothendieck ring of varieties for two families of varieties. There exist subsets of semistable and stable points so that the quotients mn d.
Jun 01, 2012 arithmetic geometry arithmetic dynamics conference. Department of mathematics and computer science unibas. We present a framework for studying the arithmetic dynamics of correspondences, and raise some questions about heights and the action of galois in. The th mathematical society of japan international research institute moduli spaces and arithmetic geometry date. An internationally recognized center for advanced studies and a national model for public doctoral education, the graduate center offers more than thirty doctoral. Princeton university library one washington road princeton, nj 085442098 usa 609 2581470. Difference between space and mathematical structure. It also explores particular types of sequence known as arithmetic progressions aps and geometric progressions gps, and the corresponding series.
More generally, one might consider iteration of a correspondence from the variety to itself. Arithmetic dynamics and dynamics on moduli spaces the following question is more of a request for pointers to suitable literature on introductory material for. Mg,n moduli space of genus g surfaces with n marked points. Moduli spaces and arithmetic dynamics crm monograph series. Algorithms in complex dynamics and mapping class groups workshop. A fundamental goal is to describe arithmetic properties in terms of underlying geometric structures.
P1, parameterized by t in a riemann surface x, and the arithmetic dynamics of f t on rational points p1k where k cx or qx. A convenient way to visual p1c is to identify it with the unit sphere in r3 by drawing lines from the north pole of the sphere to points in the xyplane. The arithmetic of dynamical systems is intended for an audience of researchers and graduate students in number theory. A complex submanifold of mg,n is totally geodesic if it contains a geodesic. Arithmetic dynamics and dynamics on moduli spaces the following question is more of a request for pointers to suitable literature on introductory material for arithmetic dynamics and dynamics on moduli spaces. Arithmetic dynamics special session joint math meetings, denver, colorado, jan 2020. According to the american heritage dictionary 1, it concerns the mathematics of integers under addition, subtraction, multiplication, division, involution, and evolution. Interval arithmetic in product spaces was originally defined by these executable formulas. The present text differs from other treatments of arithmetic in several respects. For example, i knew for long time vector spaces, then hilbert spaces, that i. Download limit exceeded you have exceeded your daily download allowance. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. Arithmetic dynamics and dynamics on moduli spaces mathoverflow. Moduli spaces of elliptic curve and abelian varieties.
Signed arithmetic extensions and new arithmetical operators. Verilog 2001 adds a power operator, represented by an token. Silverman may 5, 2020 this document lists a wide variety of articles and books in the area of arithmetic dynamics. Intersection theory on the moduli space of curves and the matrix airy function maxim kontsevich 1 communications in mathematical physics volume 147, pages 1 23 1992 cite this article. Sean lawton mason experimental geometry lab geometry labs united conference, august 2830, 2015 statement of the problem in this project, we study the dynamics of the action of. Introduction to algebraic and arithmetic dynamics rims, kyoto. With this chapters lessons, you can study finite and infinite sequences, in addition to different types of. November2,2018 we extend the well known characterization of vp ws as the class of polynomials computed by polynomial size arithmetic branching programs to other complexity classes. The graduate center, the city university of new york established in 1961, the graduate center of the city university of new york cuny is devoted primarily to doctoral studies and awards most of cunys doctoral degrees.
Towards an arithmetic for partial computable functionals. Sometimes the formula is stated with the idea that the first term is for n 0 or n 1 explicit, using subscripts. An introduction to mathematical cryptography, with jill pipher and jeffrey hoffstein, springerverlag, utm, 2008. We present a new algorithm for deciding satisfiability of nonlinear arithmetic constraints. Arithmetic and geometricprogressions mctyapgp20091 this unit introduces sequences and series, and gives some simple examples of each. In these notes, we present a connection between the complex dynamics of a family of rational functions f t. Pdf an arithmeticalgebraic work space for the promotion. The general form of uniform boundedness for preperiodic points on projective space reads as follows. Periods on arithmetic moduli spaces robert argus, patrick brown, jermain mcdermott, graduate student adviser diaaeldin taha, faculty adviser dr. Moduli spaces and arithmetic dynamics ams bookstore. In broad terms, a moduli problem consists of three ingredients.
Analysis and topology on arithmetic locally symmetric spaces. The arithmetic of dynamical systems graduate texts in. If you have not seen these subjects or want to do further reading, the books 1, 5, 15 are good introductions to complex dynamics and 2, 9, 12 are standard texts on diophantine equations and. Bibliography for arithmetic dynamics brown university. An example of an arithmetic function is the divisor function whose value at a positive integer n is equal to the number of divisors of n. This process leads to the best possible approximation of the operation in pm by that in im. In the relative trace formula approach to the arithmetic gangrossprasad conjecture, we formulate a local conjecture arithmetic transfer in the case of an exotic smooth formal moduli space of pdivisible groups, associated to a unitary group relative to a ramified quadratic extension of a padic field.
The value by which consecutive terms increase or decrease is called the common difference. The book could easily be used for a specialtopics graduate course. It will return a real number if either operand is a real value, and an integer value if both operands are integer values. A mathematical structure is a set or sets associated with some mathematical object s like a binary operation,collection of its subsets etc which satisfy some axioms. Ratn d stab ratn d ss are nonempty zariski open subsets of ratn d, i. In the higher rank case we proceed in the same way as in the case of hyperbolic manifolds. An arithmetic progression ap, also called an arithmetic sequence, is a sequence of numbers which differ from each other by a common difference. The arithmetic of dynamical systems, springerverlag, gtm 241, 2007. In such an approach, however, the connection with the powerset operations and several other interpretations, which are of fundamental interest in interval analysis, are missing. I finish todays lesson by telling students that this pattern is a particular kind of pattern called an arithmetic sequence. We can describe an arithmetic sequence with a recursive formula, which specifies how each term relates to the one before. Arithmetic dynamics is the study of the numbertheoretic properties of integer, rational, padic, and or algebraic points under repeated application of a polynomial or rational function. Round this result into the set of intervals im by taking the least interval which includes the result in pm. The rst two terms of an arithmetic sequence are 4, 10.