Articles tagged with Algebraic Geometry
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Study of abstract structures, patterns, quantities, relationships, and logical reasoning through pure and applied mathematical disciplines. Encompasses algebra, calculus, geometry, topology, number theory, analysis, discrete mathematics, mathematical logic, set theory, probability, statistics, and computational mathematics. Investigates mathematical structures, theorems, proofs, algorithms, functions, equations, and the rigorous logical frameworks underlying quantitative reasoning. Provides the foundational language and tools for all scientific fields, enabling precise description of natural phenomena, modeling of complex systems, and the development of technologies across physics, engineering, computer science, economics, and all quantitative sciences.
Anna Seigal, assistant professor at Harvard's John A. Paulson School of Engineering and Applied Sciences, has received the 2025 Sloan Research Fellowship for her work on connecting geometric invariant theory and maximum likelihood estimation in data science.
Calcea Johnson and Ne'Kiya Jackson, two U.S. high school students, have made history by publishing their first academic paper detailing five new ways of proving Pythagoras' Theorem via trigonometry. Their study reveals ten new proofs altogether, including one previously presented at a conference.
Researchers have developed big algebras, a new mathematical tool that connects abstract algebra and geometry, enabling unprecedented insights into symmetry groups. This breakthrough has the potential to strengthen the connection between quantum physics and number theory.
University of California San Diego researchers Jacques Verstraete and Sam Mattheus solve longstanding Ramsey problem r(4,t), estimating the solution as t^3. This breakthrough provides a cubic function estimate for finding four people who know each other or t people who don't, shedding light on a century-old math puzzle.
Researchers used machine learning to expand and accelerate work on 'atomic shapes,' fundamental pieces of geometry in higher dimensions. The breakthrough identifies shapes and their properties, such as dimension, accelerating new insights across Pure Mathematics.
Researchers at Rice University have developed a method to predict the shapes of crystals that lack symmetry by assigning arbitrary latent energies to their surfaces. This approach uses closure equations with arbitrary parameters to mimic nature's solution, allowing for accurate crystal shape predictions.
Bhattacharya's project uses topological abstraction to reduce complexity in robotic systems, enabling more efficient and accurate motion planning. The approach has potential applications in industries such as transportation, manufacturing, and healthcare.
The MU College of Education and Human Development offers a two-year graduate certificate program for Missouri elementary school teachers to enhance their math education teaching skills. The program focuses on collaboration, creativity, and problem-solving in the classroom to promote student confidence and positive experiences with math.
Researchers have found a fundamental connection between two basic integrable hierarchies of solitonic type, KdV and BKP, revealing surprising relationships between these equations. The discovery makes Schur Q-functions a natural basis for expansion of KdV tau-functions.
Researchers from Utah State University, Thomas Hill and Andreas Malmendier, explore the duality between F-theory and heterotic string theory in eight dimensions. They discovered four unique ways to slice K3 surfaces as Jacobian elliptic fibrations, enabling investigation of underlying physical theories.
Researchers developed an algorithm that uses first-order echoes from microphones to reconstruct a room's shape. The method is a theoretical problem but has potential applications in various fields, such as vehicle navigation and sound localization.
Researchers present a new continuous model describing self-organized criticality, integrating areas such as economics and developmental biology. The model uses tropical geometry to describe the dynamics of critical systems, providing a universal solution for phenomena like earthquakes and sandpiles.
Peter Scholze's discovery of perfectoid spaces has fundamentally expanded the range of methods used at the intersection of number theory and geometry. This award is a milestone in the long tradition of mathematics in Bonn, one of the biggest centers for mathematical teaching and research in Germany and worldwide.
Herbert Edelsbrunner, a renowned researcher in computational geometry and topology, has been awarded the 2018 Wittgenstein Prize. The prize will support his research, enabling him to establish Austria as a leading center for this field.
Researchers from the Blue Brain Project used algebraic topology to discover structures in the brain with up to eleven dimensions. These high-dimensional structures and spaces arise when a group of neurons forms a clique, generating precise geometric objects that can never be produced by chance.
David H. Yang, an MIT undergraduate, has been awarded the 2017 AMS-MAA-SIAM Morgan Prize for his exceptional research in algebraic geometry and geometric representation theory. Yang's work has been recognized for its excellence, with three papers published or in preparation in prominent mathematical journals.
Birkar, Cascini, Hacon, and McKernan's 2010 article on minimal models for log general type varieties revolutionized algebraic geometry research. The work transformed the minimal model program, marking a watershed in the field and earning them the prestigious AMS Moore Prize.
The authors' book has made algebraic geometry accessible to a broad audience, including students and researchers in many fields. The book's impact has been significant, introducing the topic to new audiences and broadening its teaching applications.
Researchers at Disney Animation Studios developed a multigrid method that speeds up cloth simulation six to eight times faster than conventional methods. The technique enables more realistic look and behavior of cloth in animations, making it suitable for simulations requiring lots of detail like clothing worn by characters.
Researchers developed a new method to analyze neural activity, revealing an organized geometric structure in neurons. The study used clique topology and found similar structure in activities among place cells in different experimental conditions.
Peter Scholze, a leading mathematician at 26, is honored for solving an important special case of the weight-monodromy conjecture. His groundbreaking work on perfectoid spaces has garnered numerous accolades, including the Prix Peccot and SASTRA Ramanujan Prize.
Robert Lazarsfeld is being awarded the 2015 AMS Steele Prize for his outstanding work in algebraic geometry, as documented in his two-volume book 'Positivity in Algebraic Geometry I and II'. The prize recognizes the profound influence of these books on research in the field over the past decade.
The American Mathematical Society has announced its prize winners, recognizing outstanding contributions to mathematics in various fields. The recipients include notable mathematicians and researchers who have made significant impacts on the field.
The DFG has approved 9 new Collaborative Research Centres (CRCs) focusing on topics such as ingestive behaviour, mathematical invariants and metal oxide-water interactions. The CRCs will receive a total of 64.4 million euros for an initial period of three years and nine months.
Graduate student Yash Lodha and Justin Moore describe geometric solution for von Neumann-Day problem, a centuries-old challenge in group theory. The solution involves a finite set of nine rules and has been hailed as natural and compelling enough to study for its own sake.
Researchers from Chinese Academy of Sciences and Tsinghua University presented additional, previously unknown geometries corresponding to all possible kinematical algebras. These geometries are classified into three relativistic geometries, absolute-time geometries, and absolute-space geometries, each with unique properties.
Chris Hacon, a distinguished University of Utah math professor, has been selected as a Simons Foundation Investigator, receiving up to $1.32 million over five years. He will support graduate students and visiting experts in algebraic geometry.
Bernd Sturmfels received the John von Neumann Lecture for his work on applying algebraic ideas to problems in biology, statistics, optimization, and polynomial systems. The lecture surveyed recent applications of abstract algebra in modeling and solving nonlinear problems.
Dieter Kotschick solved Hirzebruch's problem, determining that most Chern numbers depend on algebraic structure of a variety, not topological properties. The breakthrough resolves the relationship between flexible and rigid geometric objects.
Researchers from Florida State University, Yale University, and Princeton University developed a new theory that analyzes music using geometry. The 'geometrical music theory' tool helps composers explore uncharted possibilities and musicians may be trained differently. It represents a culmination of the marriage between music and math.
A team of music professors has devised a new way to analyze and categorize music using geometric principles. This method, known as geometrical music theory, translates musical concepts into mathematical structures, revealing hidden patterns and relationships. By assigning mathematical structure to musical families, researchers can gain...
David Mumford is recognized for his contributions to algebraic surfaces, geometric invariant theory, and the modern algebraic theory of moduli of curves and theta functions. His work has fundamentally changed algebraic geometry, laying the foundations for string theory in physics.
The American Mathematical Society has presented several prestigious prizes at the Joint Mathematics Meetings, recognizing significant achievements in mathematical exposition, research, and lifetime achievement. Notable winners include David Mumford, Karen Uhlenbeck, and Henry McKean.
Andrei Okounkov, Terence Tao and Wendelin Werner are honored with the Fields Medal for their work in probability, representation theory and algebraic geometry. Their contributions have brought new insights into problems in physics and mathematics.
Kengo Hirachi has been awarded the 2006 Bergman Prize for his deep work on the singularities of the Bergman and Szego kernels and their relationship to CR geometry. His research employs a range of tools in geometry and analysis, including complex variables and microlocal analysis.
Dr. Vladimir Voevodsky and Madhu Sudan received the prestigious awards for their innovative contributions to algebraic geometry, number theory, computer science, and probabilistically checkable proofs.