Streaming Video - Spring 2004

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MSRI: Spring 2004

Genetics of Complex Disease
February 9 - 13, 2004

Wing Wong: An approach to obtain tight clusters
Joe Gray: Genetic complexity in cancer
Adam Olshen: Change-point methods for the analysis of array-based DNA copy number data
Warren Ewens: Thoughts on the TDT
Thomas Quertermous: Microarray profiling to identify vascular wall genes for association based candidate gene studies of atherosclerosis: genomics meets genetics
Eddy Rubin: Comparing Genomes to Study Disease
Nik Schork: Novel Multivariate Analysis Methods for Genomic Analysis
Art Owen: A Gene Recommender for C. elegans
David Siegmund: Mapping QTL in the presence of gene-covariate
Terry Speed: Finding genes associated with multiple sclerosis
Benjamin Yakir: A probabilistic framework for the statistics of selective sampling
Honghzhe Li: Statistical Methods for Analysis of Microarray Time Course Gene Expression Data
Hua Tang: Inference of Ancestry for Admixed Groups
Stefan Bekiranov: Mapping of Transcription Factor Sites along Human Chromosones 21 and 22 Using Genome Tiling Arrays
Ingleif Hallgrimsdottir: Algebraic Statistical Genetics: Linkage Analysis
Josee Dupuis: Identification of polymorphisms that explain a linkage peak
Richard Olshen: Tree-structured Supervied Learning and the Genetics of Hypertension
Heping Zhang: Linkage Analysis of Longitudinal Data and Study Design Considerations
Fengzhu Sun: Haplotype Block Parition and its applications to association studies
Mark Segal: Sequence-based Prediction of HIV-1 Replication Capacity
Fred Wright: Mapping Tumor Suppressor Genes Using Loss of Heterozygosity
Sandrine Dudoit: Resampling-based multiple testing procedures: Applications to microarray data analysis
Earl Hubbell: Alleles, entropy, and locations: Which SNPs do you put on a chip?
Robert Tibshirani: Sample classification from protein mass spectroscopy by peak probability contrasts
Chao Agnes Hsiung: Normalization Methods of cDNA Microarray Experiments under Different Designs
Cheng Li: Analysis of oligonucleotide SNP array data
Karl Broman: Gene mapping in model organisms
Elizabeth Thompson: Detecting Genes from Data on Related Individuals
Chip Lawrence: A Statistical Sampling Algorithm for RNA Secondary Structure Prediction
Eleanor Feingold: Efficient simulation of p-values for linkage analysis
Hao Li: Genomic Reconstruction of Yeast Transcription Networks
Andrew Neuwald: Obtaining evolutionary clues to protein structural mechanisms
Chiara Sabatti: Dictionary models for regulatory regions in DNA and gene expression arrays
Ken Lange: Association Testing with Mendel
Richard Karp: Combinatorial Approaches to the Haplotype Phasing Problem
Matthew Stephens: Identifying recombination hotspots from LD in the human genome

Topology and Geometry of Real Algebraic Varieties
February 23 - 27, 2004

Grigory Mikhalkin: Topology and Geometry of Real Algebraic Varieties
Joost van Hamel: Galois equivariant intersection homology
Timur Sadykov: The amoeba of a discriminant
Frederic Mangolte: Real alegebraic morphisms on 2-dimensional conic bundles
Janos Kollar: Real Fano 3-folds
Stepan Orevkov: On braid monodromy monoid
Maxim Kazarian: On several classical enumerative problems in algebraic geometry
Igor Kalinin: Cohomology characteristics of real algebraic varieties
Dmitry Novikov: Convex-concave hypersurfaces in real projective spaces
Clint McCrory: A weight filtration for real algebraic varieties
Boris Shapiro: Real analogs of Hurwitz numbers
Jean-Yves Welschinger: Spinor states of real rational curves in real algebraic convex 3-manifolds and enumeratice invariants
Sergei Finashin: Real Lefschetz pencils and genus bounds for membranes
Henry King: Isotoping submanifolds to subvarieties
Ilia Itenberg: Topology of real tropical varieties
Eugenii Shustin: A tropical computation of the Weischinger invariant
Claude Michel Viterbo: Geometry of lagrangian submanifolds
Jean-Claude Hausmann: Polygon spaces
Johannes Huismann: The geometry of real space curves
Patrick Gilmer: Arf-invariants of links and congruences for real algebraic curves
S. Friedland: Applications of topology and geometry to matrices

Assessing Students' Mathematical Learning: Issues, Costs and Benefits
March 7 - 10, 2004

David Eisenbud, Deborah Ball: A Private Universe (54-sec. clip) Welcome, overview and purposes of workshop
Robert Moses, Judith Ramaley, Alan Schoenfeld, Susan Sclafani: Crucial contemporary social, political, and cultural issues in mathematics assessment in the U.S.
Hyman Bass: What is mathematical proficiency? Multiple perspectives - Part 1
Jim Milgram, Alan Schoenfeld: What is mathematical proficiency? Multiple perspectives - Part 2
Bruce Alberts: Mathematics and Science Education: Parallel National Challenges
Deborah Ball, Brandon Peoples: Live interview session (with sixth grade student)
Tim Boerst, Roger Howe: Discuss and analyze the interview with student; report back in plenary; commentators
Dick Askey, Hugh Burkhardt, Linda Fisher, Jan de Lange, Bernie Madison: What mathematical proficiency is important to measure? (content, skills, and practices, broadly defined)
Dick Askey, Hugh Burkhardt, Linda Fisher, Jan de Lange, Bernie Madison: What mathematical proficiency is important to measure? (content, skills, and practices, broadly defined) - Question and Answer Period
Heidi Boley, David Foster, William McCallum, Mark Saul, Ann Shannon, Hung-Hsi Wu: Investigation of alternative approaches to assessment of different aspects of proficiency in algebra
Alan Tucker: The New York State Regents examination: An analysis and response
Michèle Artigue, Dick Askey, Hugh Burkhardt, Linda Fisher/David Foster, Jan de Lange, Bernie Madison, Ann Shannon: Specific instruments and approaches for assessing mathematical proficiency: Plenary panel of workshop leaders
Lee Shulman: Talk: Observations midway in the conference
Ross Green, Betsy Taleporos, Mark Wilson: Issues of reliability and validity at any scale, or with any type of assessment
Phil Daro, Lily Wong Fillmore, Judit Moschkovich: Challenges of making assessments equitable and fair: Issues of culture, language, context and experience
Heidi Boley, Elizabeth Stage, Betsy Taleporos, Uri Treisman: How can large-scale state assessment programs affect educational programs?
Michèle Artigue, Heidi Boley, Bill McCallum, Robert Moses, Elizabeth Stage: Closing session: Perspectives on the workshop and next steps in an agenda related to assessment
Robert Moses: Children Left Behind: New Curricula, Large Scale Assessment and the Algebra Project

Mathematical Neuroscience
March 15 - 19, 2004

Bard Ermentrout: Slow and Steady Wins the Game: Consequences of fast rising slowly decaying excitation
Jonathan Rubin: Activity Patterns in Purely Excitatory Networks
Carson Chow: Self-sustained localized neural activity
David McLaughlin: Scale-up and the Visual Cortex
Ken Miller: The Role of Dominant Feedforward Inhibition in Layer 4 Processing
William Troy: Bumps and Waves in a Two Dimensional Neural Model
Steve Coombes: Neural networks with space-dependent delays
David Golomb: A model of frequency-dependent latency in the thalamorcortical response of the rat vibrissa system
J. Leo van Hemmen: Synchrony, pattern Formation, and the Adiabatic Principle: How Neuronal and Synaptic Dynamics Cooperate on Different Time Scales
John Rinzel: Subthreshold mechanisms for precise temporal processing
David Terman: Firing Patterns in the Subthalamopallidal Network
Marty Golubitsky: Coupled System, Gaits and Synchrony
David Hansel: Neuronal Synchrony and the Interplay between Cellular Properties, Electrical and Inhibitory Synapses
Shun-ichi Amari: How singularity affects learning and decision in neural networks
Paul Bressloff: Euclidean shift-twist symmetry in nonlocal population models
Rajesh Rao: Probabilistic Computation in Neural Circuits
Adrienne Fairhall: Adaptation over many timescales
Dmitri Chklovskii: Wiring of the Cortical Column
Carl van Vreeswijk: Heterogeneity and Contrast Invariance in Primary Visual Cortex
Nick Swindale: Coverage, Polymaps and the Visual Cortex
Fred Wolf: Is there one brain for each of us? - Multistability and symmetry in the dynamics of cortical plasticity
Zhaoping Li: A saliency map in primary visual cortex

Symplectic Geometry and Mathematical Physics
March 22 - 26, 2004

D. Salamon: Instanton Floer homology with Lagrangian boundary conditions
Y. Ruan: Recent Advances in Orbifold Theory
M. Aganagic: Topological Strings and Integrable Hierarchies
M. Hutchings: Embedded Contact Homology of T^3
Y. Eliashberg: Subcritical manifolds
Y. G. Oh: The obstruction to the A-infinity algebra and the Landau-Ginzburg superpotential: the Fano toric case
A. Givental: Quantum cobordisms and formal group laws
D. McDuff: Extensions of the Hamiltonian group
A. Kapustin: Topological strings and generalized complex geometry
F. Lalonde: A natural Floer theory withoug obstruction
G. Mikhalkin: Tropical Jacobians
I. Smith: Symplectic geometry of the adjoint quotient, I
D. Joyce: Abelian categories and stability conditions
Y. Karshon: Torus actions on blowups of CP^2
K. Hori: Orientifolds: An introduction
W. D. Ruan: Degeneration of Kahler-Einstein manifolds and minimal Lagrangian (coisotropic) vanishing cycles
B. Siebert: Toward combinatorial curve counting via maximal degenerations
M. Gross: Affine manifolds and degenerations of Calabi-Yau manifolds
P. Ozsvath: Holomorphic disks and low-dimensional topology
Ron Fintushel: Invariants for lagrangian tori in 4-manifolds
X. Liu: Genus 2 Gromov-Witten invariants
M. Usher: Lefschetz fibrations and pseudoholomorphic curves
P. Seidel: Symplectic geometry of the adjoint quotient, II

Algorithmic, Combinatorial and Applicable Real Algebraic Geometry
April 12 - 16, 2004

Doug Lind: Dynamics and tropical varieties
Federico Ardila: Tropical linear varieties and phylogenetic trees
David Speyer: f-Vectors of Tropical Linear Spaces
Thorsten Theobald: Some constrained polynomial optimization problems in nonlinear computational geometry
Dima Pasechnik: Univariate representations and algebraic sets over quadratic maps
Jean Lasserre: A moment approach to analyze zeros of triangular polynomial maps
James Demmel: On deciding whether a real polynomial can be evaluated accurately in rounded arithmetic
Evgenia Soprunova: Lower bounds for some sparse polynomial systems
Benoit Bertrand: Upper bounds for some sparse polynomial systems
Maurice Rojas: Some New Complexity Bounds for Real Fewnomials
Jim Ruffo: Conjectures and Experimentation in the Real Schubert Calculus
Alexandre Eremenko: Real Wrosnki map
John Keyser: Implementing Algebraic Routines in Exact Solid Modeling
Matthias Drton: Polynomial optimization in multivariate statistics
Ruchira Datta: How Many Totally Mixed Nash Equilibria Can Graphical Games Have
Luis David Garcia Puente: Algebraic Geometry Applications in Model Selection
Rimas Krasauskas: Bezier curves and patches on toric surfaces
Danielle Gondard-Cozette: On the number of connected components of smooth real varieties
Hartwig Bosse: Semi-algebraic representations of polyhedra
Jesus de Loera: Real zeros of Erhart polynomials
Tomas Recio: Hypercircles and Units
Fabrice Rouillier: Exact Computations and Real Roots of Polynomial Systems
Sanjay Lall: Sum of squares and decentralized stochastic decision problems
Grigoriy Blekherman: There are Significantly More Nonnegative Polynomials Than Sums of Squares
Markus Schweighofer: Barrier functions and cones of positive semidefinite forms
Salma Kuhlman: On G-invariant moment problems
Monique Laurent: Moment matrices, radical ideas, and optimization
Pablo Parrilo: SOS optimization: exploiting structure and a new approach

Geometric Combinatorics
May 23 - 27, 2004

Francis Su: Lecture 1- Combinatorial Convexity
Francis Su: Lecture 2- Set Intersections & Helly's Theorem
Francis Su: Lecture 3- Polytopes I: Examples & Construction
Francis Su: Lecture 4- Polytopes II: Polar Duality
Michael Gage: Cross-Program Lecture- WeBWork
Francis Su: Lecture 5- Polytopes III: Combinatorics of Faces
Francis Su: Lecture 6- Polytopes IV: Counting Faces
Francis Su: Lecture 7- Simplicial Complexes & Triangulations
Francis Su: Lecture 8- Combinatorial Fixed Point Theorems I: Sperner's Lemma
Francis Su: Lecture 9- Combinatorial Fixed Point Theorems II: Tucker's Lemma
Francis Su: Lecture 10- Combinatorial Fixed Point Theorems III: Kneser Colorings
Francis Su: Lcture 11- Combinatorial Fixed Point Theorems IV: Trees
Francis Su: Lecture 12- An Introduction to Phylogenetic Trees
Francis Su: Lecture 13- What is Tropical Geometry
Francis Su: Lecture 14- Minkowski's Theorem
Francis Su: Lecture 15- What are Ehrhart Polynomials?

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	Streaming Video - Spring 2004 Introduction \| Hints for Viewing \| Other SV Sites \| CDROMs and Video Tapes for sale \| Mirror Sites Welcome to the MSRI Video Archive, Click on the triangle icons to expand/contract the list. MSRI: Spring 2004 Genetics of Complex Disease February 9 - 13, 2004 Wing Wong: An approach to obtain tight clusters Joe Gray: Genetic complexity in cancer Adam Olshen: Change-point methods for the analysis of array-based DNA copy number data Warren Ewens: Thoughts on the TDT Thomas Quertermous: Microarray profiling to identify vascular wall genes for association based candidate gene studies of atherosclerosis: genomics meets genetics Eddy Rubin: Comparing Genomes to Study Disease Nik Schork: Novel Multivariate Analysis Methods for Genomic Analysis Art Owen: A Gene Recommender for C. elegans David Siegmund: Mapping QTL in the presence of gene-covariate Terry Speed: Finding genes associated with multiple sclerosis Benjamin Yakir: A probabilistic framework for the statistics of selective sampling Honghzhe Li: Statistical Methods for Analysis of Microarray Time Course Gene Expression Data Hua Tang: Inference of Ancestry for Admixed Groups Stefan Bekiranov: Mapping of Transcription Factor Sites along Human Chromosones 21 and 22 Using Genome Tiling Arrays Ingleif Hallgrimsdottir: Algebraic Statistical Genetics: Linkage Analysis Josee Dupuis: Identification of polymorphisms that explain a linkage peak Richard Olshen: Tree-structured Supervied Learning and the Genetics of Hypertension Heping Zhang: Linkage Analysis of Longitudinal Data and Study Design Considerations Fengzhu Sun: Haplotype Block Parition and its applications to association studies Mark Segal: Sequence-based Prediction of HIV-1 Replication Capacity Fred Wright: Mapping Tumor Suppressor Genes Using Loss of Heterozygosity Sandrine Dudoit: Resampling-based multiple testing procedures: Applications to microarray data analysis Earl Hubbell: Alleles, entropy, and locations: Which SNPs do you put on a chip? Robert Tibshirani: Sample classification from protein mass spectroscopy by peak probability contrasts Chao Agnes Hsiung: Normalization Methods of cDNA Microarray Experiments under Different Designs Cheng Li: Analysis of oligonucleotide SNP array data Karl Broman: Gene mapping in model organisms Elizabeth Thompson: Detecting Genes from Data on Related Individuals Chip Lawrence: A Statistical Sampling Algorithm for RNA Secondary Structure Prediction Eleanor Feingold: Efficient simulation of p-values for linkage analysis Hao Li: Genomic Reconstruction of Yeast Transcription Networks Andrew Neuwald: Obtaining evolutionary clues to protein structural mechanisms Chiara Sabatti: Dictionary models for regulatory regions in DNA and gene expression arrays Ken Lange: Association Testing with Mendel Richard Karp: Combinatorial Approaches to the Haplotype Phasing Problem Matthew Stephens: Identifying recombination hotspots from LD in the human genome Topology and Geometry of Real Algebraic Varieties February 23 - 27, 2004 Grigory Mikhalkin: Topology and Geometry of Real Algebraic Varieties Joost van Hamel: Galois equivariant intersection homology Timur Sadykov: The amoeba of a discriminant Frederic Mangolte: Real alegebraic morphisms on 2-dimensional conic bundles Janos Kollar: Real Fano 3-folds Stepan Orevkov: On braid monodromy monoid Maxim Kazarian: On several classical enumerative problems in algebraic geometry Igor Kalinin: Cohomology characteristics of real algebraic varieties Dmitry Novikov: Convex-concave hypersurfaces in real projective spaces Clint McCrory: A weight filtration for real algebraic varieties Boris Shapiro: Real analogs of Hurwitz numbers Jean-Yves Welschinger: Spinor states of real rational curves in real algebraic convex 3-manifolds and enumeratice invariants Sergei Finashin: Real Lefschetz pencils and genus bounds for membranes Henry King: Isotoping submanifolds to subvarieties Ilia Itenberg: Topology of real tropical varieties Eugenii Shustin: A tropical computation of the Weischinger invariant Claude Michel Viterbo: Geometry of lagrangian submanifolds Jean-Claude Hausmann: Polygon spaces Johannes Huismann: The geometry of real space curves Patrick Gilmer: Arf-invariants of links and congruences for real algebraic curves S. Friedland: Applications of topology and geometry to matrices Assessing Students' Mathematical Learning: Issues, Costs and Benefits March 7 - 10, 2004 David Eisenbud, Deborah Ball: A Private Universe (54-sec. clip) Welcome, overview and purposes of workshop Robert Moses, Judith Ramaley, Alan Schoenfeld, Susan Sclafani: Crucial contemporary social, political, and cultural issues in mathematics assessment in the U.S. Hyman Bass: What is mathematical proficiency? Multiple perspectives - Part 1 Jim Milgram, Alan Schoenfeld: What is mathematical proficiency? Multiple perspectives - Part 2 Bruce Alberts: Mathematics and Science Education: Parallel National Challenges Deborah Ball, Brandon Peoples: Live interview session (with sixth grade student) Tim Boerst, Roger Howe: Discuss and analyze the interview with student; report back in plenary; commentators Dick Askey, Hugh Burkhardt, Linda Fisher, Jan de Lange, Bernie Madison: What mathematical proficiency is important to measure? (content, skills, and practices, broadly defined) Dick Askey, Hugh Burkhardt, Linda Fisher, Jan de Lange, Bernie Madison: What mathematical proficiency is important to measure? (content, skills, and practices, broadly defined) - Question and Answer Period Heidi Boley, David Foster, William McCallum, Mark Saul, Ann Shannon, Hung-Hsi Wu: Investigation of alternative approaches to assessment of different aspects of proficiency in algebra Alan Tucker: The New York State Regents examination: An analysis and response Michèle Artigue, Dick Askey, Hugh Burkhardt, Linda Fisher/David Foster, Jan de Lange, Bernie Madison, Ann Shannon: Specific instruments and approaches for assessing mathematical proficiency: Plenary panel of workshop leaders Lee Shulman: Talk: Observations midway in the conference Ross Green, Betsy Taleporos, Mark Wilson: Issues of reliability and validity at any scale, or with any type of assessment Phil Daro, Lily Wong Fillmore, Judit Moschkovich: Challenges of making assessments equitable and fair: Issues of culture, language, context and experience Heidi Boley, Elizabeth Stage, Betsy Taleporos, Uri Treisman: How can large-scale state assessment programs affect educational programs? Michèle Artigue, Heidi Boley, Bill McCallum, Robert Moses, Elizabeth Stage: Closing session: Perspectives on the workshop and next steps in an agenda related to assessment Robert Moses: Children Left Behind: New Curricula, Large Scale Assessment and the Algebra Project Mathematical Neuroscience March 15 - 19, 2004 Bard Ermentrout: Slow and Steady Wins the Game: Consequences of fast rising slowly decaying excitation Jonathan Rubin: Activity Patterns in Purely Excitatory Networks Carson Chow: Self-sustained localized neural activity David McLaughlin: Scale-up and the Visual Cortex Ken Miller: The Role of Dominant Feedforward Inhibition in Layer 4 Processing William Troy: Bumps and Waves in a Two Dimensional Neural Model Steve Coombes: Neural networks with space-dependent delays David Golomb: A model of frequency-dependent latency in the thalamorcortical response of the rat vibrissa system J. Leo van Hemmen: Synchrony, pattern Formation, and the Adiabatic Principle: How Neuronal and Synaptic Dynamics Cooperate on Different Time Scales John Rinzel: Subthreshold mechanisms for precise temporal processing David Terman: Firing Patterns in the Subthalamopallidal Network Marty Golubitsky: Coupled System, Gaits and Synchrony David Hansel: Neuronal Synchrony and the Interplay between Cellular Properties, Electrical and Inhibitory Synapses Shun-ichi Amari: How singularity affects learning and decision in neural networks Paul Bressloff: Euclidean shift-twist symmetry in nonlocal population models Rajesh Rao: Probabilistic Computation in Neural Circuits Adrienne Fairhall: Adaptation over many timescales Dmitri Chklovskii: Wiring of the Cortical Column Carl van Vreeswijk: Heterogeneity and Contrast Invariance in Primary Visual Cortex Nick Swindale: Coverage, Polymaps and the Visual Cortex Fred Wolf: Is there one brain for each of us? - Multistability and symmetry in the dynamics of cortical plasticity Zhaoping Li: A saliency map in primary visual cortex Symplectic Geometry and Mathematical Physics March 22 - 26, 2004 D. Salamon: Instanton Floer homology with Lagrangian boundary conditions Y. Ruan: Recent Advances in Orbifold Theory M. Aganagic: Topological Strings and Integrable Hierarchies M. Hutchings: Embedded Contact Homology of T^3 Y. Eliashberg: Subcritical manifolds Y. G. Oh: The obstruction to the A-infinity algebra and the Landau-Ginzburg superpotential: the Fano toric case A. Givental: Quantum cobordisms and formal group laws D. McDuff: Extensions of the Hamiltonian group A. Kapustin: Topological strings and generalized complex geometry F. Lalonde: A natural Floer theory withoug obstruction G. Mikhalkin: Tropical Jacobians I. Smith: Symplectic geometry of the adjoint quotient, I D. Joyce: Abelian categories and stability conditions Y. Karshon: Torus actions on blowups of CP^2 K. Hori: Orientifolds: An introduction W. D. Ruan: Degeneration of Kahler-Einstein manifolds and minimal Lagrangian (coisotropic) vanishing cycles B. Siebert: Toward combinatorial curve counting via maximal degenerations M. Gross: Affine manifolds and degenerations of Calabi-Yau manifolds P. Ozsvath: Holomorphic disks and low-dimensional topology Ron Fintushel: Invariants for lagrangian tori in 4-manifolds X. Liu: Genus 2 Gromov-Witten invariants M. Usher: Lefschetz fibrations and pseudoholomorphic curves P. Seidel: Symplectic geometry of the adjoint quotient, II Algorithmic, Combinatorial and Applicable Real Algebraic Geometry April 12 - 16, 2004 Doug Lind: Dynamics and tropical varieties Federico Ardila: Tropical linear varieties and phylogenetic trees David Speyer: f-Vectors of Tropical Linear Spaces Thorsten Theobald: Some constrained polynomial optimization problems in nonlinear computational geometry Dima Pasechnik: Univariate representations and algebraic sets over quadratic maps Jean Lasserre: A moment approach to analyze zeros of triangular polynomial maps James Demmel: On deciding whether a real polynomial can be evaluated accurately in rounded arithmetic Evgenia Soprunova: Lower bounds for some sparse polynomial systems Benoit Bertrand: Upper bounds for some sparse polynomial systems Maurice Rojas: Some New Complexity Bounds for Real Fewnomials Jim Ruffo: Conjectures and Experimentation in the Real Schubert Calculus Alexandre Eremenko: Real Wrosnki map John Keyser: Implementing Algebraic Routines in Exact Solid Modeling Matthias Drton: Polynomial optimization in multivariate statistics Ruchira Datta: How Many Totally Mixed Nash Equilibria Can Graphical Games Have Luis David Garcia Puente: Algebraic Geometry Applications in Model Selection Rimas Krasauskas: Bezier curves and patches on toric surfaces Danielle Gondard-Cozette: On the number of connected components of smooth real varieties Hartwig Bosse: Semi-algebraic representations of polyhedra Jesus de Loera: Real zeros of Erhart polynomials Tomas Recio: Hypercircles and Units Fabrice Rouillier: Exact Computations and Real Roots of Polynomial Systems Sanjay Lall: Sum of squares and decentralized stochastic decision problems Grigoriy Blekherman: There are Significantly More Nonnegative Polynomials Than Sums of Squares Markus Schweighofer: Barrier functions and cones of positive semidefinite forms Salma Kuhlman: On G-invariant moment problems Monique Laurent: Moment matrices, radical ideas, and optimization Pablo Parrilo: SOS optimization: exploiting structure and a new approach Geometric Combinatorics May 23 - 27, 2004 Francis Su: Lecture 1- Combinatorial Convexity Francis Su: Lecture 2- Set Intersections & Helly's Theorem Francis Su: Lecture 3- Polytopes I: Examples & Construction Francis Su: Lecture 4- Polytopes II: Polar Duality Michael Gage: Cross-Program Lecture- WeBWork Francis Su: Lecture 5- Polytopes III: Combinatorics of Faces Francis Su: Lecture 6- Polytopes IV: Counting Faces Francis Su: Lecture 7- Simplicial Complexes & Triangulations Francis Su: Lecture 8- Combinatorial Fixed Point Theorems I: Sperner's Lemma Francis Su: Lecture 9- Combinatorial Fixed Point Theorems II: Tucker's Lemma Francis Su: Lecture 10- Combinatorial Fixed Point Theorems III: Kneser Colorings Francis Su: Lcture 11- Combinatorial Fixed Point Theorems IV: Trees Francis Su: Lecture 12- An Introduction to Phylogenetic Trees Francis Su: Lecture 13- What is Tropical Geometry Francis Su: Lecture 14- Minkowski's Theorem Francis Su: Lecture 15- What are Ehrhart Polynomials? 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