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#Polynomial Method

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Institute for Advanced Study

The Polynomial Method and the Restriction Problem - Larry Guth

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Explore the polynomial method and restriction problem in mathematics, featuring insights on visualizing concepts, analyzing proofs, and examining algebraic potential.
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9 Lesons
54 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

The Restriction Problem and the Polynomial Method - Lecture 2

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Explore Stein's restriction conjecture, Kakeya conjecture, and polynomial method in harmonic analysis. Understand wave packet decomposition and intersection of tubes in Fourier analysis.
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1 Lesons
58 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Basic Lower Bounds and Kneser's Theorem by David Grynkiewicz

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Explore set addition, basic lower bounds, and Kneser's Theorem in additive combinatorics. Learn key proofs, including Cauchy-Davenport theorem, and applications to field extensions.
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15 Lesons
54 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Additive Number Theory - Extremal Problems and the Combinatorics of Sumsets by M. Nathanson

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Explore extremal problems and combinatorics of sumsets in additive number theory, covering density, lower bounds, Cauchy-Davenport theorem, and Erdos-Turan conjecture.
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24 Lesons
50 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

The Restriction Problem and the Polynomial Method - Lecture I

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Explore Stein's restriction conjecture, the Kakeya conjecture, and the polynomial method in harmonic analysis. Learn about wave packet decomposition and its applications in studying hypersurface-supported functions.
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17 Lesons
55 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Marina Iliopoulou- Three Polynomial Methods for Point Counting, Lecture II

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Explore three powerful polynomial methods for point counting: Dvir's Kakeya problem solution, Guth-Katz's polynomial partitioning, and the slice rank method for arithmetic progressions.
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12 Lesons
1 hour 1 minute
On-Demand
Free-Video
Hausdorff Center for Mathematics

Marina Iliopoulou - Three Polynomial Methods for Point Counting, Lecture I

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Explore three powerful polynomial techniques for point counting: Dvir's method, polynomial partitioning, and slice rank method, with applications in finite fields and geometry.
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10 Lesons
54 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Marina Iliopoulou- Three Polynomial Methods for Point Counting, Lecture III

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Explore advanced polynomial techniques for solving geometric problems, including Dvir's method, polynomial partitioning, and slice rank method in finite-field settings.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Hausdorff Center for Mathematics

The Restriction Problem and the Polynomial Method - Lecture IV

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Explore Stein's restriction conjecture, Kakeya conjecture, and the polynomial method in restriction theory. Understand wave packet decomposition and intersection of tubes in hypersurfaces.
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1 Lesons
59 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

The Restriction Problem and the Polynomial Method - Lecture III

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Explore Stein's restriction conjecture, Kakeya conjecture, and the polynomial method in restriction theory. Understand wave packet decomposition and intersection of tubes in hypersurfaces.
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1 Lesons
57 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Valentin Blomer: The Polynomial Method for Point Counting and Exponential Sums

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Explore advanced techniques for counting points on curves over finite fields and estimating exponential sums using families of auxiliary polynomials.
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1 Lesons
1 hour
On-Demand
Free-Video
Hausdorff Center for Mathematics

The Polynomial Method for Point Counting and Exponential Sums

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Explore how auxiliary polynomials aid in counting points on curves over finite fields and estimating exponential and character sums.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
International Centre for Theoretical Sciences

Endpoint Eigenfunction Bounds for the Hermite Operator by Sanghyuk Lee

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Explore endpoint eigenfunction bounds for the Hermite operator, delving into advanced harmonic analysis concepts and recent developments in mathematical research.
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1 Lesons
1 hour 55 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Global Maximizers for Spherical Restriction by Diogo Oliveira e Silva

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Explore global maximizers for spherical restriction in harmonic analysis. Gain insights into recent developments and techniques in this cutting-edge mathematical field.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

New Characterizations of Sobolev Spaces by Po Lam Yung

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Explores novel approaches to characterizing Sobolev spaces, advancing understanding in functional analysis and partial differential equations. Presents cutting-edge research in harmonic analysis.
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1 Lesons
2 hours 7 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Global Solutions with Asymptotic Self-Similar Behaviour for the Cubic Wave by Giuseppe Negro

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Explore asymptotic self-similar behavior in global solutions for cubic wave equations. Delve into advanced harmonic analysis techniques and their applications in mathematical physics.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Exponentials Rarely Maximize Fourier Adjoint Restriction Estimates on Cones by Giuseppe Negro

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Explore Fourier adjoint restriction estimates on cones, focusing on the rarity of exponential maximizers. Gain insights into advanced harmonic analysis techniques and their applications.
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1 Lesons
46 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Points and Distances by Malabika Pramanik

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Explore geometric relationships between points and distances in harmonic analysis. Discover recent developments in Fourier restriction, polynomial methods, and discrete analysis techniques.
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1 Lesons
1 hour 18 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Maximal Functions Associated to Families of Curves in the Plane by Joshua Zahl

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Explore maximal functions related to curve families in the plane, delving into harmonic analysis techniques and recent developments in this mathematical field.
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1 Lesons
1 hour 20 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Regularized Inverse Brascamp-Lieb Inequalities

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Explores advanced mathematical concepts in harmonic analysis, focusing on regularized inverse Brascamp-Lieb inequalities. Offers insights into cutting-edge research and applications in theoretical mathematics.
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1 Lesons
1 hour 36 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Estimates for Bochner-Riesz Means at the Critical Index by David Beltran

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Explore advanced harmonic analysis techniques, focusing on Bochner-Riesz means estimates at the critical index. Gain insights into cutting-edge research and applications in this specialized mathematical field.
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1 Lesons
1 hour 52 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Modern Trends in Harmonic Analysis

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Explore cutting-edge developments in harmonic analysis, focusing on polynomial methods and discrete harmonic analysis. Gain insights from expert lectures and research talks on recent breakthroughs and future prospects.
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1 Lesons
1 hour 52 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Modern Trends in Harmonic Analysis

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Explore cutting-edge developments in harmonic analysis, focusing on polynomial methods and discrete analysis. Gain insights from expert lectures and research talks on sharp restriction estimates, quadrature rules, and more.
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1 Lesons
1 hour 40 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Pointwise Ergodic Theorems for Non-Conventional Polynomial Averages by Benjamin Krause

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Explore advanced ergodic theory with a focus on non-conventional polynomial averages, delving into pointwise convergence theorems and their applications in harmonic analysis.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Discussion of Montgomery's Large Value Problem by Larry Guth

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Exploration of Montgomery's Large Value Problem, delving into advanced harmonic analysis concepts and recent developments in the field of mathematics.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Quadrature Rules on Manifolds - Partitions by Giacomo Gigante

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Explore advanced quadrature techniques for manifolds, focusing on partition methods. Gain insights into cutting-edge harmonic analysis research and its applications in mathematical problem-solving.
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1 Lesons
54 minutes
On-Demand
Free-Video
BIMSA

Progression-Free Sets in Arithmetic Sequences

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Explore lower and upper bounds for progression-free sets in $\mathbb{Z}_m^n$, examining the polynomial method's application to $r_k(\mathbb{Z}_m^n)$ and related problems.
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1 Lesons
48 minutes
On-Demand
Free-Video
Google TechTalks

Algorithms and Hardness for Attention and Kernel Density Estimation

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Explore algorithmic techniques for Attention and Kernel Density Estimation, examining fast algorithms and hardness results to optimize computational efficiency in machine learning and statistical tasks.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video