| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | February 3, 2015 |
| Latest Amendment Date: | February 3, 2015 |
| Award Number: | 1502166 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Andrew Pollington
adpollin@nsf.gov (703)292-4878 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | February 15, 2015 |
| End Date: | January 31, 2016 (Estimated) |
| Total Intended Award Amount: | $24,500.00 |
| Total Awarded Amount to Date: | $24,500.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
615 W 131ST ST NEW YORK NY US 10027-7922 (212)854-6851 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
Rm 509, MC 4406, 2990 Broadway New York NY US 10027-6902 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | ALGEBRA,NUMBER THEORY,AND COM |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
This award provides funding for the workshop "Perspectives on Complex Algebraic Geometry" to take place May 22-25, 2015 at Columbia University, New York, New York. Algebraic Geometry is the study of the solutions of polynomial equations in several variables. As polynomials arise in every topic that can be studied numerically, algebraic geometry plays a central role within mathematics and has close ties to the sciences. The field traces its roots back to the foundations of mathematics, has led to some of the most significant mathematical accomplishments in the past hundred years, and continues to be a burgeoning and vital field today. Within the field of algebraic geometry, complex algebraic geometry plays a special role. Namely, the complex structure of the solution sets allows for a wide range of techniques, including those from geometry, analysis, and topology. Some of the most powerful techniques involve the use of Hodge theory, which uses harmonic theory on compact manifolds to relate the topology, complex structure, and algebraic properties of the solutions sets. Recently, the connections with physics have played an increasingly important role in algebraic geometry. Many questions in physics can be phrased naturally in the language of differential geometry. Through deep and surprising connections that exist between differential geometry and complex algebraic geometry, some of these questions can be addressed using the techniques of algebraic geometry. Questions posed by physicists have been solved using techniques developed by algebraic geometers. In turn, recent developments in physics have led to astonishing new results and open problems in algebraic geometry.
The purpose of the workshop is to survey the recent developments in the field of complex algebraic geometry with a focus on the following 3 main topics: (1) Topology and geometry of algebraic surfaces and 4-manifolds, (2) Vector bundles and G-bundles, and (3) Geometric applications of Hodge theory. These are central topics in the field of complex algebraic geometry, that have seen a number of interesting recent developments, and lie at the intersection of a number of fields of mathematics, but which have been less well represented lately in terms of workshops. The workshop will bring together some of the leading experts in the field, as well as a number of young researchers, who will further propel developments in these directions. More details on the conference can be found at its website: https://sites.google.com/site/complexalgebraicgeometry/.
PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
The Perspectives on Complex Algebraic Geometry workshop was held May 22-25, 2015 at Columbia University. The workshop was attended by about 70 algebraic geometers, from around the world, including England, Germany, France, Italy, and China, with about 20 of those being junior participants.
The purpose of the workshop was to survey the recent developments in the field of Complex Algebraic Geometry with a focus on the following 3 main topics: (1) Topology and Geometry of Algebraic Surfaces and four manifolds, (2) Vector bundles and principal bundles, and (3) Geometric applications of Hodge theory. These are central topics in the field of complex algebraic geometry, that have seen a number of interesting recent developments, and lie at the intersection of a number of fields of mathematics, but which have been less well represented lately in terms of workshops. Thus, it was an opportune time to hold such an event. The workshop brought together some of the leading experts in the field, as well as a number of young researchers, and we expect this will further propel developments in these directions. The workshop also served as an occasion to celebrate the contributions of Robert Friedman (Columbia University); his work has had a tremendous influence on the topics that were the themes of this workshop.
In summary, regarding the intelectual merrit of the project, the workshop brought together various points of view in Complex Algebraic Geometry and related fields. While the workshop had its focus in theoretical Complex Algebraic Geometry, the topics have connections with other fields of mathematics, as well as physics. While the themes of the workshop are at the forefront of recent developments in the field of complex algebraic geometry, some of the topics have been much less well represented recently in terms of conferences, and consequently represent huge potential for growth. We expect the conference will spark further interactions, lead to the discovery of new connections, and the establishment of new research directions. This is one of the primary ways in which the conference will provide a braoder impact, namely, the conference will be highly influential in other fields beyond complex algebraic geometry, most notably topology, complex geometry, and physics.
Last Modified: 04/20/2016
Modified by: Sebastian B Casalaina-Martin
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