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# Adv Algebra MATH 711

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This 21 page Class Notes was uploaded by Mrs. Preston Lehner on Thursday October 29, 2015. The Class Notes belongs to MATH 711 at University of Michigan taught by Staff in Fall. Since its upload, it has received 12 views. For similar materials see /class/231500/math-711-university-of-michigan in Mathematics (M) at University of Michigan.

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Date Created: 10/29/15

310400pm 310500pm 410500pm 410600pm 210300pm 310400pm 410500pm 500600pm 310400pm 310400pm 310400pm 410530pm 410600pm 1200100pm 210300pm 310400pm 310400pm 310400pm 310500pm 410500pm 410500pm 410500pm Fall 2007 University of MichiganDepartment of Mathematics httpwwwmathlsaumicheduseminarsindexshtml Ann Arbor MI 481091043 September 17th September 23rd Monday September 17 Student Analysis Seminar Nina White UM HausdorffDimension 3866 EH Number Theory and Representation Theory Seminar Skip Garibaldi Emory U Bilinear forms invariant under algebraic groups 4096 EH Several Complex Variables Seminar Debraj Chakrabarti U of Western Ontario Holomorphic Extension of CR functions from Quadratic Cones 3096 EH Geometry amp Physics Aleksey Zinger StoneyBrook The Geometry of GenusOne GromovWitten Invariants and Mirror Symmetry 4088 EH Tuesday September 18 I What is Seminar TBA 3096 EH Geometry Seminar Brett Parker M IT Holomorphic curves adiabatic limits and the exploded category 4088 EH Colloquium Yves Benoist Ecole Normale Superieure Paris Rational points on symmetric varieties 1360 H Social Hour Upper Atrium Wednesday September 19 I Student Arithmetic Seminar Craig Spencer UM TBA 3866 EH Student AIM Seminar Selim Esedoglu UM amp Anna Gilbert UM Internships in Industry 3096 EH Geometric Function Theory Seminar Roger W Barnard Texas Tech How far can you deform a disk under a convex map 4096 EH Working Seminar in Several Complex Variables and Complex Dynamics John Erik Fornaess UM Short 2 4088 EH Algebraic Geometry Seminar Carl Miller UM F crystas on characteristicp curve 3088 EH Thursday September 20 I Mathematical Biology Richard Yamada UM A Chemical Kinetic Model of Transcriptional Elongation 4096 EH Student Algebraic Geometry Seminar Eugene Eisenstein UM Bend amp Break 3866 EH Commutative Algebra Seminar Mel Hochster UM Tor Ext and local cohomoogy continued 3096 EH FinancialActuarial Mathematics Seminar Hao Xing UM Pricing Asian options for jump diffusions 3088 H Topology Seminar Jose GOmez UM Higher Twistings in Ktheory 4096 EH Study Seminar Mario Bonk UM The mapping class group 4088 EH Differential Equations Peter Miller UM The Semicassica Modi ed Nonlinear Schr odinger Equation Facts and Artifacts 4096 EH Math Club Renzo Cavalieri UM When points want to smash together but we don t let them 2quotd Floor Nesbitt Room Student Combinatorics Kelli Talaska UM Young Tabeaux and the Littlewood Richardson Rule 3866 EH Friday September 21 I 10501200pm EECS Theory Seminar TBA CSE 3941 31104100pm 31104100pm 31104100pm 41 05100pm Complex Analysis Seminar Roger Barnard Texas Tech U and UM An isoperirnetric inequality for logarithmic capacity 4088 EH Applied and Interdisciplinary Mathematics Seminar Andrew Belmonte Penn State Acoustic ripples on long entrained bubbles 1084 EH Student GeometryTopology Diane Vavrichek UM Stallings Theorem 3096 EH Combinatorics Hannah Markwig UM Counting place elliptic tropical curves with fixedjinvariant 3866 EH UPCOMING EVENTS Ziwet Lecture e 8 Speaker Curtis McMullen Rainich Lecture Mar 18 2008 Speaker Gang Tian ABSTRACTS FOR THE WEEK OF SEPT 17 SEPT 23 2007 Student Analysis Seminar Monday Sept 17 310400pm 3866 EH Nina White UM Hausdorff Dimension What is dimension We are used to thinking of dimension of a space as being a natural number In the case of dimension of a vector space or even topological dimension this is true Hausdorff dimension is a notion of dimension which corresponds to topological dimension in wellbehaved spaces like Euclidean space but takes fractional values in crazier fractal spaces In this talk we39ll define Hausdorff measure Hausdorff dimension and make some explicit calculations I39ll assume a basic knowledge of measure 0 the ry Department of Mathematics Bulletin 91707 thru 92307doc Number Theory and Representation Theory Seminar Monday Sept 17 310500pm 40 6 Skip Garibaldi Emory U Bilinear forms invariant under algebraic groups For representations of semisimple Lie algebras over the complex numbers there is a wellknown criterion in terms of highest weights for whether the representation has a symmetric bilinear form that is invariant under the action ofthe Lie algebra ie whether the representation is orthogonal If it is then the bilinear form is uniquely determined up to a scalar These results are easily extended to irreducible representations of semisimple algebraic groups over arbitrary fields For nonsplit groups the bilinear form gives some information about the group One famous example is the Killing form for simple Lie algebras over the real numbers It turns out that these invariant forms are already interesting for groups of type A1 Several Complex Variables Seminar Monday September 17 410500pm E Debraj Chakrabarti U of Western Ontario Holomorphic Extension of CR functions from Quadratic Cones We consider holomorphic extension properties of CR functions defined on real submanifolds with singularities It is proved that for a a quadratic cone M a CR function admits onesided extension iff it does not have two sided support a geometric condition that generalizes minimality in the sense of Tumanov Geometry amp Physics Monday September 17 410600pm 088 EH Aleksey Zinger StoneyBrook The Geometry of GenusOne GromovWitten Invariants and Mirror Symmetry The mirror symmetry principle of string theory has led to astounding predictions for counts of holomorpic curves The verification ofthe original 1991 prediction for genus0 GWinvariants of a quintic threefold Q3 in the mid 1990s was quickly followed by proofs of MS formulas for genus0 invariants of other manifolds On ther other hand the 1993 genus1 BCOV prediction for Q3 and other positivegenus MS formulas remained elusive until recently I will describe geometric properties of genus1 invariants that make them about as computable as genus0 invariants In particular they lead to the proof ofthe genus1 BCOV prediction for Q3 by applying the classical localization theorem The first hour will consist of a general overview of everything involved except forthe localization part In the second hour I am planning to discuss the localization computation which in a sense is a reduction to genus 0 but I39d be happy to talk about details of any ofthe geometric properties ifthis is preferred by the audience Department of Mathematics Bulletin 91707 thru 92307doc Geometry Seminar Tuesday September 18 310400pm 4088 EH Brett Parker MIT Holomorphic curves adiabatic limits and the exploded category The exploded category is an extension ofthe smooth category with a good holomorphic curve theory in which some degenerations39 appear in smooth families I will explain how this is useful for the study of pseudoholomorphic curves and the relationship between the exploded category and tropical geometry Colloquium Tuesday September 18 410500pm 1360 EH Yves Benoist Ecole Normale Superieure Paris Rational points on symmetric varieties I will describe the polar decomposition of symmetric spaces both over the real and the padic fields I will explain how such a decomposition allows one to prove equidistribution results for the rational points on symmetric varieties Student AIM Seminar Wednesday September 19 310400pm 3096 EH Selim Esedoglu UM amp Anna Gilbert UM ntemships in Industry At this week39s meeting Profs Selim Esedoglu and Anna Gilbert will talk about internships how to find them how to get involved and what to expect from them Several students will give short presentations on their internship experiences this past summer All math graduate students are welcome both pure and applied Geometric Function Theory Seminar Wednesday September 19 31000pm 4096 Roger W Barnard Texas Tech How far can you deform a disk undera convex map In this talk we discuss how we apply variational techniques and special function theory to verify some conjectures of C Pommerenke39s and of D Minda on the sharp upper bound for the Schwarzian derivative of hyperbolically convex maps This completes the classification ofthe exteremal domains for the Schwarzian in all three classical geometries hence answering the question first posed in the 5039s as to how far one can distort a disk under a convex map in Euclidean spherical and hyperbolic geometries Department of Mathematics Bulletin 91707 thru 92307doc Working Seminar in Several Complex Variables and Complex Dynamics Wednesday September 19 410530pm 4088 EH John Erik Fornaess UM Short 6 We construct domains in C2 which have some characteristic features of C2 but who nevertheless are not biholomorphic to C2 Student Algebraic Geometry Seminar Thursday September 20 210300pm 3 Eugene Eisenstein UM Bend amp Break Mori39s bend and break techniques are a collection of lemmas that all revolve around a simple and very geometric idea a curve that bends with some appropriate number of points fixed must in the limit break off into a rational component and some other curves This talk will explain some ofthe reasons the lemmas are important and prove a few ofthem Next week we will apply these lemmas to show that Fano varieties have a rational curve through every point Time permitting I will outline the proofthat Fano varieties are rationally connected there is a rational curve through any two points Commutative Algebra Seminar Thursday September 20 310400pm 3 Mel Hochster UM Tor Ext and local cohomology continued For the first several weeks of the semester I will be giving some talks on elementary homological algebra the functors Tor and Ext and then an introductory treatment of local cohomology I will write up these lectures and make them available from my Web page This is intended to supplement the background of students in Math 711 but others who are interested in this material are welcome FinancialActuarial Mathematics Seminar Thursday September 20 310400pm 3088 EH Hao Xing UM Pricing Asian options for jump diffusions In this talk I will discuss the pricing problem for the European Asian options in jump diffusion models Following the method which Prof Bayraktar used to solve the problem for American options a sequence of functions are also constructed to approximate the price of Asian options However because the payoff functions are not necessarily bounded new methods are introduced to prove the regularity of functions in this sequence As a result this sequence of functions converge unformly and exponentially fast to the price of Asian option on compact sets This provides us a fast numerical algorithm At the end ofthis talk I will present the numerical performance of this algorithm for Merton39s model and Kou39s model This is a joint work with Erhan Bayraktar Department of Mathematics Bulletin 91707 thru 92307doc Topology Seminar Thursday September 20 310400pm 4 6 EH Jos Gomez UM Higher Twistings in Ktheory In this talk I will discuss the socalled higher twistings for twisted Ktheory It is known that for a compact space X twistings of Ktheory over X are classified by XBGL1K Here GL1K Z2X KZ2X BSU is the space of units of K with Hspace structure induced by the tensor product of vector bundles The twistings corresponding to the factor XBBSU are called higher twistings In the talk I will give a definition for the most general twistings of Ktheory This has been worked out rigorously on the literature only for the lower twistings and only sketched for the general situation The idea of the construction is to consider a category consisting of Fredholm operators for different Hilbert space to get a semigroup I will also discuss the equivariant setting limited to the case over a point I will show that if G is a compact Lie group then there are no higher twistings for completed twisted Gequivariant Ktheory over a point I contrast one can see that this is not the case for topological groups in general Study Seminar Thursday September 20 310500pm 4088 EH Mario Bonk UM The mapping class group Let S be a smooth closed simply connected 2manifold By definition the mapping class group of S is the quotient MS Homeoquot SHomeo0S where Homeo S is the group of all orientation preserving homeomorphisms on S and Homeo0S is the group of all homeomorphisms on S isotopic to the identity This talk is the first of a lecture series that will provide an introduction to this subject Differential Equations Thursday September 20 410500pm 4 6 EH Peter Miller UM The Semiclassical Modi ed Nonlinear Schrlquotodinger Equation Facts and Artifacts I will discuss some recent work joint with J DiFranco on semiclassical Cauchy problems for an integrable perturbation of the focusing nonlinear Schr quotodinger equation The perturbation is singular in the sense of inversescattering and also in the more practical sense that the modified equation admits solutions with surprisingly different properties than the unmodified equation quotFacts and Artifactsquot is a reference to a similarlytitled paper by E V Doktorov whose lecture on the subject in Edinburgh in 2004 originally piqued our interest Department of Mathematics Bulletin 91707 thru 92307doc Math Club Thursday September 20 410500pm 2quot Floor Nesbitt Room Renzo Cavalieri UM When points want to smash together but we don t let them In this talk we will explore a few ideas about moduli spaces ie spaces those points naturally parameterize geometrical objects such as circles in the plane lines in 3space etc This means two things i there is a natural bijection between the points ofX and the objects we wish to study ii close points parameterize similar objects Our toy example will be the space of configurations of n points on the sphere We will explicitly investigate and describe this space and then see that it has unpleasant properties full of holes rips and tears To patch the situation literally we are confronted with a fundamental problem in moduli space theory namely how to meaningfully enlarge the class of objects being parameterized so as to obtain a more beautiful and useful moduli space Student Combinatorics Thursday September 20 410500pm 3866 EH Kelli Talaska UM Young Tableaux and the LittlewoodRichardson Rule Using Young tableaux and jeu de taquin we will give a combinatorial characterization of the Littlewood Richardson coefficients found in representation theory and algebraic geometry We will look at some concrete examples and iftime permits we will discuss other combinatorial descriptions andor variations of the LittlewoodRichardson Rule Complex Analysis Seminar Friday September 21 310400pm 4088 EH Roger Barnard Texas Tech U and UM An isoperimetric inequality for logarithmic capacity We discuss our proof using symmetrizations and variational techniques of a sharp lower bound for the logarithmic capacity of a compact connected planar set E in terms of its area and diameter Our result includes as special cases Faber39s inequality cap E gt diam E4 and Polya39s inequality cap E gt sqrtarea EPi This is joint work with K Pearce and AY Solynin Department of Mathematics Bulletin 91707 thru 92307doc 310400pm 310400pm 310500pm 410500pm 410600pm 500630pm 210300pm 310400pm 310400pm 310400pm 310400pm 410500pm 310400pm 310400pm 310400pm 310400pm 410530pm 410600pm 1210100pm 210300pm 210300pm 310400pm 310400pm 310400pm 310400pm 410500pm 410500pm Fall 2007 University of MichiganDepartment of Mathematics httpwwwmathsaumicheduseminarsindexshtml Ann Arbor MI 481091043 October 15th October 21st Monday October 15 Student Analysis Seminar Not meeting this week 3866 EH Topics in Algebraic Geometry Seminar Not meeting this week 2866 EH Number Theory and Representation Theory Seminar Not meeting this week 4096 EH Several Complex Variables Seminar Not meeting this week 3096 EH Geometry amp Physics Not meeting this week 4088 EH Teaching Mathematics Not meeting this week 3088 EH Tuesday October 16 I What is quotSeminar Selim Esedoglu UM Whatis the MumfordShah functional 3096 EH Geometry Seminar Not meeting this week 4088 EH Algebra Seminar Not meeting this week 3096 EH Algebraic Geometry Seminar Special Lectures on Branchvarieties Allen Knutson UCSD Schubert varieties in GB are normal and CohenMacaulay 3088 EH Student Representation TheoryLie Theory Seminar Not meeting this week 4096 EH Colloquium Not meeting this week 1360 EH Wednesday October 17 Student Arithmetic Seminar Wansu Kim UM TBA 3866 EH Student AIM Seminar Special Seminar Ice Cream Social 3096 EH Working Group in Integrable Systems and Asymptotics Peter Miller UM Orthogonal polynomials in the complex plane dbar problems and random normal matrices 4088 EH Geometric Function Theory Seminar Steffen Rohde U of Washington Random Quasiconforma Maps 4096 EH Working Seminar in Several Complex Variables and Complex Dynamics Andrei lordan Institut de Mathematiques de Jussieu Compex tangential curves of constant curvature in the unit ball of 2 and homogeneous polynomials 4088 EH Algebraic Geometry Seminar Claude Sabbah Ecole Polytechnique An extension of Hodge theory 3088 EH Thursday October 18 Mathematical Biology Seminar Daniel Forger UM TBA 4096 EH Student Algebraic Geometry Seminar Wansu Kim UM An Overview of Deligne llusie 2 3866 EH Study Seminar Pt 1 Pekka Pankka UM The mapping class group V 3096 EH Study Seminar Pt 2 Pekka Pankka UM The mapping class group V cont 4 88 EH FinancialActuarial Mathematics Seminar Not meeting this week 3088 EH Commutative Algebra Seminar Mel Hochster UM Tor Ext and local cohomoogy continued 3096 EH Topology Seminar Xiaojun Chen UM A chain model of the free loop space and string topology 4096 EH Differential Equations TBA 4088 EH Math Club Jeff Lagarias UM The 3X1 Probem 2quotd Floor Nesbitt Room I Thursday October 18 continued I 410500pm Student Combinatorics Dave Anderson UM Tropical Geometry ll 3866 EH Friday October 19 10501200pm EECS Theory Seminar Anupam Gupta Carnegie Mellon Univ MaxMin Facility Location and Set Coverage Problems Stream CSE 3941 310400pm Applied and Interdisciplinary Mathematics Seminar Alex Powell Vanderbilt Rounding algorithms for redundant signal expansions 1084 EH 31 04100pm Student GeometryTopology Dave Constantine UM Quasiisometries of symmetric spaces 3096 EH 41 05100pm Combinatorics Vladimir Retakh Rutgers Algebras associated to directed acyclic graphs 3866 EH EVENTS THIS WEEK Midwest Dynamical Systems Conference FridaySunday October 1921 2007 Organizer Carl Simon Center for the Study of Complex Systems amp UM AI sessions in 1360 EH Titles and schedule listed on the back pages of the bulletin OSUIUM Algebraic Geometry Workshop Saturday amp Sunday October 20 amp 21 2007 B844 EH Speakers Patrick Brosnan William Fulton Sandor Kovacs Mihnea Popa Titles and schedule TBA UPCOMING EVENTS Rainich Lecture Jan 1517 2008 Speaker Gang Tian Ziwet Lecture e 8 Speaker Curtis McMuIIen Department of Mathematics Bulletin 101507thru102107doc ABSTRACTS FOR THE WEEK OF OCT 15 OCT 21 2007 What is quotSeminar Tuesday October 16 210300pm 3 96 EH Selim Esedoglu UM What is the MumfordShah functional Mumford and Shah39s variational model for image segmentation is one of the best known and influential mathematical models in image processing and computer vision It poses image segmentation which means partitioning a given image into regions containing distinct objects as an optimization problem It has been adapted to many other applications since its inception both in and outside of image processing Its analysis and computation motivated lots of interesting mathematics I will describe some of these Algebraic Geometry Seminar Special Lectures on Branchvarieties Tuesday October 16 310400pm 3 88 Allen Knutson UCSD Schubert varieties in 65 are normal and CohenMacaulay I39ll use a variant of the second theorem from the last lecture to give an inductive and wholly geometric proof ofthis fact usually proved using Frobenius splitting Another proof using very little sheaf cohomology was given by Brion The proof also implies the following any Schubert variety is covered by Tinvariant open affine patches which have flat Tequivariant degenerations to StanleyReisner schemes This had been known for various flavors of Grassmannians but doesn39t seem to have been observed before in this generality Geometric Function Theory Seminar Wednesday October 17 310400pm 4 Steffen Rohde U of Washington Random Quasiconformal Maps I will explain how random homeomorphisms appear naturally in the study of Schramm39s Loewner evolution SLE via conformal welding in the SLE trace and how qc maps could be useful in the study of SLE Then I will discuss two toy models for random qc maps Department of Mathematics Bulletin 101507thru102107doc Working Seminar in Several Complex Variables and Complex Dynamics Wednesday October 17 410530pm 4088 EH Andrei lordan Institut de Mathematiques de Jussieu Complex tangential curves of constant curvature in the unit ball of C and homogeneous polynomials We prove that a nonconstant homogeneous polynomial P on C2 having the property that P1 on a complextangential real analytic curve ofthe boundary of the unit ball reduces to a monomial by a unitary change of variables This is a positive answer to conjectures of HO Kim Algebraic Geometry Seminar Wednesday October 17 410600pm H Claude Sabbah Ecole Polytechnique An extension of Hodge theory In this talk I will introduce the notion of variation of twistor structure as an extension ofthe notion of variation of Hodge structure following C Simpson I will explain the usefulness ofthis notion for proving the decomposition theorem for projective morphisms and semisimple representations ofthe fundamental group of quasiprojective varieties over the complex numbers after the work of T Mochizuki and myself I will end with some perspective on semisimple representations of the wild fundamental group Student Algebraic Geometry Seminar Thursday October 18 210300pm 3 Wansu Kim UM An Overview of DeligneIllusie 2 The degeneration ofthe Hodge spectral sequence for a smooth proper scheme of characteristic 0 is a basic fact in algebraic geometry Since the statement can be made purely algebraic ie it can be stated without using any complex analysis it is natural to expect a purely algebraic proof In this talk I would like to present a purely algebraic proof of this fact following Delignelllusie3987 This proof is quite surprising in two aspects First the proof is by reduction to the case where the base field is of positive characteristic Note that there are many examples of smooth projective surfaces in positive characteristic for which the degeneration ofthe Hodge spectral sequence fails to hold Delignelllusie proved the degeneration in positive characteristic under extra hypotheses upper bound on dimension and liftability from which they deduced the statement in characteristic 0 Second the proof is short and elementary contrary to our expections on Deligne Illusie and characteristic p The key technical inputs are 1 Cartier Isomorphism 3957 by Cartier different proof by Grothendieck and 2 basic deformation theory and none ofthem are hard results From the characteristic p statement one can deduce Kodaira vanishing theorem for smooth projective schemes both in characteristic p under extra hypotheses and in characteristic 0 by the argument due to Raynaud It is worth noting that the proof is important not just because it gives a purely algebraic proof of the degeneration of Hodge spectral sequence but because it provides a useful tool to study algebraic geometry in positive characteristic To minimize the background I will state and hopefully provide some intuition on certain properties of smooth morphisms we need Spectral sequences will not appear in the proof Department of Mathematics Bulletin 101507thru102107doc Study Seminar Pt 1 amp Pt 2 Thursday October 18 Pt 1 210300 amp Pt 2 310400 Pt 1 3096 EH amp Pt 2 4088 EH Pekka Pankka UM The mapping class group V Let S be a smooth closed simply connected 2manifold By definition the mapping class group of S is the quotient MS Homeo SHomeo0S where Homeo S is the group of all orientation preserving homeomorphisms on S and Homeo0S is the group of all homeomorphisms on S isotopic to the identity In this talk we continue the discussion on the NielsenThurston trichotomy of mapping classes Commutative Algebra Seminar Thursday October 18 310400pm 3 Mel Hochster UM Tor Ext and local cohomology continued For the first several weeks of the semester I will be giving some talks on elementary homological algebra the functors Tor and Ext and then an introductory treatment of local cohomology I will write up these lectures and make them available from my Web page This is intended to supplement the background of students in Math 711 but others who are interested in this material are welcome Topology Seminar Thursday October 18 310400pm 4096 EH Xiaojun Chen UM A chain model of the free loop space and string topology In this talk we will study the Frobenius structure on the chain complex of a smooth manifold and then construct a chain and also the equivariant chain model of its free loop space From such a chain complex we show that there is a BatalinVilkovisky algebra on its homology which models the string topology of ChasSullivan Some ofthe other structures on the loop space and their applications will also be discussed Math Club Thursday October 18 410500pm 2nd Floor Nesbitt Room Jeff Lagarias UM The 3x1 Problem The notorious 3x1 problem considers the function Cn on positive integers if n is even divide by 2 and if n is odd multiply by 3 and add 1 so C2nn C2n16n4 The 3x1 Conjecture or Collatz problem is to show that starting from any positive integer n and iterating this function long enough you will get to 1 and then cycle through 1 4 2 This problem is unsolved Despite its simple statement it could well be the hardest problem in mathematics The talk will discuss why it is probably true and why it is a really hard problem Department of Mathematics Bulletin 101507thru102107doc EECS Theory Seminar Friday October 19 10501200pm CSE 3 41 Anupam Gupta Carnegie Mellon Univ MaxMin Facility Location and Set Coverage Problems Stream Consider the following problem you want to locate kfacilities to serve some set of demands arriving tomorrow Unfortunately you do not precisely know what the demand set will be you merely know that it will be one of M potential demand sets S1 SM given to you in advance and that the actual demand set Si will be chosen from these M sets by an adversary after seeing your solution Where should you place your facilities We consider the problems of locating these k facilities to minimize the worstcase cost suffered or to maximize the worstcase profit collected and give greedystyle algorithms for several such problems This is based on work with Barbara Anthony Vineet Goyal Carlos Guestrin Andreas Krause Viswanath Nagarajan all at Carnegie Mellon University and Brendan MacMahan at Google Pittsburgh Applied and Interdisciplinary Mathematics Seminar Friday October 19 300400pm 1 08 Alex Powell Vanderbilt Rounding algorithms for redundant signal expansions Redundancy is a key to practical and reliable data representation in many settings Frame theory provides a mathematical framework for stably representing signals as linear combinations of an overcomplete collection of quotbasic building blocksquot We shall discuss the problem of quantization analog todigital conversion for redundant finite frame expansions Our focus will be on a special class of algorithms known as SigmaDelta schemes which are related to error diffusion We explain the basics of how SigmaDelta schemes work in this setting and point to current directions of research including error estimates stability theorems and reconstruction procedures Student GeometryTopology Friday October 19 310400pm 0 6 E Dave Constantine UM Quasiisometries of symmetric spaces In this talk 39 survey a result by Kleiner and Leeb stating that a quasiisometry of a higher rank symmetric space is a finite distance from an isometry The talk will be a very loose sketch ofthe proof with a focus on the many diverse tools from analysis geometry topology and even logic that go into proving it Besides quasiisometries we39ll see biLipschitz maps asymptotic cones ultrafilters buildings local homology groups etc Department of Mathematics Bulletin 101507thru102107doc Combinatorics Friday October 19 410500pm 3866 Vladimir Retakh Rutgers Algebras associated to directed acyclic graphs We construct and study a class of algebras associated to generalized layered graphs ie directed graphs with a ranking function on their veitices and edges Each finite directed acyclic graph admits a structure of a generalized layered graph We construct linear bases in such algebras compute their Hilbert series and discuss their Koszulity and other properties Our interest to generalized layered graphs and algebras associated to those graphs is motivated by their relations to factorizations of polynomials over noncommutative rings This is 39oint work with Robert Wilson Department of Mathematics Bulletin 101507thru102107doc Tentative Schedule and Arrangements Midwest Dynamical Systems Conference October 1921 2007 The University of Michigan Organizer Carl Simon Center for the Study of Complex Systems and Department of Mathematics All sessions in 1360 East Hall Friday October 19 2250 Anthony Bloch Michigan Integrable Geodesic Flows 0n the symmetric and skewsymmetric matrices 3350 Sebastian Marotta Boston University Singular Perturbations of z 9 zAn with Multiple Poles Refreshments 4450 Steve Batterson Emory The Grandfather of American Mathematics and the Dynamics of Meteor Showers 5550 Youngna Choi Montclair State Attractors 0f TwoPiece Expanding Maps Saturday October 20 In Celebration of the almost Fortieth Anniversary of the August 1968 Berkeley Global Analysis Conference 9945 John Franks Northwestern Global Fixed Points for Surface Actions and Morita s Theorem 101050 Robert F Williams Texas Higher Dimensional Continued Fractions and Positive Matrices 111 1 50 Chris Novak Northwestern Distortion elements and Discontinuity Growth in the Interval Exchange Group 12l30 Lunch 130220 Morris Hirsch WisconsinBerkeley TBA 230320 Charles Pugh Toronto Focal Stability with Mauricio Peixoto Department of Mathematics Bulletin 101507thru102107doc 310400pm 310500pm 410500pm 410600pm 210300pm 310400pm 410500pm 310400pm 310400pm 310500pm 410530pm 410600pm 210300pm 310400pm 310400pm 310400pm 410500pm 410500pm 410500pm 410530pm 11 001200pm 310400pm Fall 2007 University of MichiganDepartment of Mathematics httpwwwmathsaumicheduseminarsindexshtml Ann Arbor MI 481091043 September 10th September 16th Monday September 10 Student Analysis Seminar Short Organizational Meeting 3866 EH Number Theory and Representation Theory Seminar Chris Hall UM Tate s conjecture in bers of a pencil 4096 EH Several Complex Variables Seminar Lina Lee UM Asymptotic behavior ofinvariant metrics 3096 EH Geometry amp Physics Eric Zaslow Northwestern Constructibe Sheaves and the Fukaya Category 4088 EH Tuesday September 11 I Seminar Alejandro Uribe UM What is Spectral Geometry What is 3096 EH Geometry Seminar Zhou Zhang UM Kaeher Ricci flow and complex Mange Ampere equation 4088 EH Colloquium Marina Rather UC Berkeley The theory of Unipotent Flows on homogeneous spaces of Lie groups with emphasis on applications 1360 EH Wednesday September 12 Student Arithmetic Seminar Organizational Meeting Student AIM Seminar Not meeting this week 3396 Geometric Function Theory Seminar Mario Bonk UM Quasiconforma flows 4096 EH Working Seminar in Several Complex Variables and Complex Dynamics Not meeting this week 4088 EH Algebraic Geometry Seminar Benjamin Howard UM Nice projective embeddings for the GIT quotients PA1quotn SL2 3088 EH 3866 EH EH Thursday September 13 I Student Algebraic Geometry Seminar Kevin Tucker UM Proximity Matrices and Easy Surface Resolution Computations 3866 EH Commutative Algebra Seminar Mel Hochster UM Tor Ext and local cohomoogy EH FinancialActuarial Mathematics Seminar Erhah Bayraktar UM On the nite horizon American option pricing problem A proof of smoothness and an exponentialy fast converging scheme 3088 EH Topology Seminar Not meeting this week 4096 EH Differential Equations Jeffrey Rauch UM Exponential Growth for Wave Equations with Positive Compacty Supported Potentials 4096 EH Math Club Brian Conrad UM The 17gon 2quotd Floor Nesbitt Room Student Combinatorics Florian Block UM Hidden Markov Models Newton Polytopes Tropical Math and Googe 4088 EH Panel on Grant and Fellowship Applications Special Seminar Present by UM Panel A Barvihok S Esedoglu D Forger M Mustata et al 3088 EH Friday September 14 EECS Theory Seminar Erin Rhode UM TBA CSE 3941 Applied and Interdisciplinary Mathematics Seminar Santiago Schnell Indiana U How do cells form rounded segments 1084 EH Friday September 14 continued I 31104100pm Student GeometryTopology Nina White UM Introduction to geometric group theory 096 EH 41 05100pm Combinatorics Lauren Williams Harvard Toric geometry and the totally non negative part of GP 3866 EH UPCOMING EVENTS Ziwet Lecture e 8 Speaker Curtis McMullen Rainich Lecture Mar 18 2008 Speaker Gang Tian ABSTRACTS FOR THE WEEK OF SEPT 10 SEPT 16 2007 Student Analysis Seminar Monday Sept 10 310400pm 3866 EH Short Organizational Meeting This week39s seminar will be a halfhour organizational meeting We will discuss which topics people are interested in hearing about during the coming semester so that we can plan some 2 4 week quotthemesquot in addition to our usual individual talks We will end in time for departmental tea at 345 Number Theory and Representation Theory Seminar Monday Sept 10 310500pm 4096 EH Chris Hall UM Tate s conjecture in bers of a pencil Let k be a finitely generated field and E a nonisotrivial elliptic curve over kt If k is finite then the functionfield analogue of a conjecture of Goldfeld asserts that the average rank of all quadratic twists of E is welldefined and equal to 2 If k is infinite then we prove that this average rank is welldefined and equals 0 At the heart of the proof is a theorem which asserts that for most oneparameter families of twists almost all kfibers ofthe family have rank 0 The methods used to prove the theorem apply to other oneparameter families of varieties and in particular they allow one to show that the Tate conjectures are true for almost all kfibers in the family Department of Mathematics Bulletin 91007 thru 91607doc Several Complex Variables Seminar Monday September 10 410500pm 3096 EH 0 Asymptotic behavior of invariant metrics As a point inside a domain moves toward the boundary biholomorphically invariant metrics behave according to the characteristics ofthe domain If a domain is holomorphically convex one naturally expects it to be complete with respect to invariant metrics and the metric blowing up near the boundary We explore the asymptotic behavior of invariant metrics near the boundary of pseudoconvex domains which are known to be holomorphically convex and show that the metrics blow up at a rate that is determined by the geometry ofthe boundary Geometry amp Physics Monday September 10 410600pm 88 EH Eric Zaslow Northwestern Constructible Sheaves and the Fukaya Category I will describe an equivalence between these two categories focusing on simple examples The talk is based on work of Nadler and joint work with Nadler What is quotSeminar Tuesday September 11 210300pm Alejandro Uribe UM What is Spectral Geometry In this talk I will survey problems and results about the relationship between the spectrum ofthe Laplace Beltrami operator on a compact Riemannian manifold and the geometry ofthe manifold Geometry Seminar Tuesday September 11 310400pm 4088 EH Zhou Zhang UM KaehlerRicci ow and complex MangeAmpere equation The complex version of the Ricci flow the KaehlerRicci flow known to be equivalent to a scalar evolution equation is relatively simple looking in comparison to the tensor evolution equation of the original Ricci flow The equation is indeeed the timedependent version of the complex MongeAmpere equation which determinants and so is highly nonlinear Pluripotential theory ofthe MongeAmpere operator naturally arises in the study of this problemThe relation to Algebraic Geometry can be seen as the motivation and goal Department of Mathematics Bulletin 91007 thru 91607doc Colloquium Tuesday September 11 410500pm Marina Ratner UC Berkeley The theory of Unipotent Flows on homogeneous spaces of Lie groups with emphasis on applications In the last few years there has been a tremendous upsurge in applications ofthe theory of Unipotent flows on homogeneous spaces of Lie groups to various problems arising from different areas of mathematics In this talk I will present the main results ofthe theory and then discuss a number of important applications The talk will be accessible to a general audience familiar with the notion of a Lie group and its quotients with respect to discrete subgroups Geometric Function Theory Seminar Wednesday September 12 310500pm 4 9 Mario Bonk UM Quasiconformal ows A vector field generates a quasiconformal flow if its so called strain tensor is essentially bounded I will give a survey on this subject and discuss some related open problems Student Algebraic Geometry Seminar Thursday September 13 210300pm 3866 EH Kevin Tucker UM Proximity Matrices and Easy Surface Resolution Computations This talk will give an overview of the ZariskiLipman theory of complete ideals in the local ring of a point on a smooth surface In particular we will talk about proximity matrices and their use in computations of embedded resolutions in two dimensions We will also talk about the relation to the germs of analytically irreducible curves If there is time we will mention Jarvilehto39s use of the theory to compute the jumping numbers of these ideals Commutative Algebra Seminar Thursday September 13 310400pm 3 Mel Hochster UM Tor Ext and local cohomology For the first several weeks of the semester I will be giving some talks on elementary homological algebra the functors Tor and Ext and then an introductory treatment of local cohomology I will write up these lectures and make them available from my Web page This is intended to supplement the background of students in Math 711 but others who are interested in this material are welcome Department of Mathematics Bulletin 91007 thru 91607doc FinancialActuarial Mathematics Seminar Thursday September 13 310400pm 3088 EH Erhan Bayraktar UM On the nite horizon American option pricing problem A proof of smoothness and an exponentially fast converging scheme We give a new proof of the fact that the value function ofthe finite time horizon American put option for a jump diffusion when the jumps are from a compound Poisson process is the classical solution of a quasivariational inequality and it is CA1 across the optimal stopping boundary Our proof only uses the classical theory of parabolic partial differential equations of Friedman and does not use the theory of vicosity solutions since our proof relies on constructing a sequence of functions each of which is a value function of an optimal stopping time for a diffusion The sequence is constructed by iterating a functional operator that maps a certain class of convex functions to smooth functions satisfying variational inequalities orto value functions of optimal stopping problems involving only a diffusion The approximating sequence converges to the value function exponentially fast therefore it constitutes a good approximation scheme since the optimal stopping problems for diffusions can be readily solved Math Club Thursday September 13 410500pm 2quot Floor Nesbitt Room Brian Conrad UM The 17gon At the end of the 18th century the teenage Gauss stunned the mathematical world by constructing a new regular polygon with straightedge and compass Whereas the ancient Greeks could construct regular triangles squares and pentagons in this way and some others easily made from these by bisecting sides etc no further progress had been made in 2000 years on whether or not it was possible to construct a regular 7gon or beyond Gauss insight was that this apparently geometric problem is really a problem in arithmetic and that to discover new constructions or prove impossibility results in this direction one had to carry out an arithmetic rather than geometric investigation In this talk we will explain some basic construction principles that translate the geometric problem into algebra and then we show how to use some arithmetic to actually carry out the construction of a regular 17gon Student Combinatorics Thursday September 13 410500pm 4 8 EH Florian Block UM Hidden Markov Models Newton Polytopes Tropical Math and Google We will explain the Hidden Markov Model as it is used in algebraic statistics and its connection to Google39s quotDid you meanquotfeature This turns out to be equivalent to the evaluation of a tropical polynomial which can be done efficiently by Minkowski decomposition of a newton polytope Department of Mathematics Bulletin 91007 thru 91607doc Panel on Grant and Fellowship Applications Special Seminar Thursday September 13 410530pm Present by UM Panel Alexander Barvinok Selim Esedoglu Danny Forger Mircea Mustata et al 30 8 EH This panel discussion is aimed at helping new postdoctoral faculty in the process of applying for grants and fellowships Others are welcome Applied and Interdisciplinary Mathematics Seminar Friday September 14 310400pm 1084 EH Santiago Schnell lndiana U How do cells form rounded segments The vertebral column develops during early embryogenesis It is formed from a periodic pattern of somites along the anterior posterior axis of an organism These somites are rounded structures formed after compaction and segmentation of mesenchymal cells There is an intricate pattern of gene activity and protein expression which appears to be involved in the rounding process However here we consider the physical aspects of the mechanism Current theory is that increased cellcell adhesion induces minimization ofthe tissue surface tension yielding rounded tissue We investigate this behaviour using a viscous liquid model oftissue dynamics Given the relatively brieftime in which somite formation occurs and the high bulk viscosities of tissues the basic model is unconvincing We propose a simple chemotactic mechanism to extend the model This new model successfully produces rounding within the timeframe found in vivo abstract continued on next page Applied and Interdisciplinary Mathematics Seminar abstract continued This work was recently published in Developmental Biology The reference is R Grima S Schnell 2007 Can tissue surface tension drive somite formation Developmental Biology 307 248257 This manuscript doesn39t have any hard mathematics We have published a number of papers on somitogenesis a number of them are for a mathematical inclined audience The most recent mathematical model we developed is the clock and wavefront model for somite formation The references with the mathematical model and its analysis are R E Baker S Schnell P K Maini 2006 A clock and wavefront mechanism for somite formation Developmental Biology 293 116126 R E Baker S Schnell P K Maini 2006 A mathematical investigation ofa new model for somitogenesis Journal of Mathematical Biology 52 458482 These two papers are related to the topic of my talk somitogenesis though there are not directly dealing with the same problem I39ll explain what we have done and show some of the models Then I39ll go to our new theories which at the moment we haven39t developed yet into full mathematical models We simply have done physiochemical calculations to test different theories This will give a flavour ofthe new biological problems and the opportunities open to applied mathematicians Department of Mathematics Bulletin 91007 thru 91607doc

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