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 Algebraic cycles and crystalline cohomology
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Faculty Research Virginia Math Bulletin. Loading seminars The results of this work will be disseminated through papers that will first be uploaded on both the arXiv and my homepage at the Mathematical Department's website to ensure a fast and efficient dissemination of the research in order to maximize their usefulness and impact to academia.
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The results of this work will then be published in leading international journals to attest the quality of the research and increase the prestige of both the EPSRC and the Host Institution. The knowledge will also be shared through the PI's travels to conferences and seminars, as well as by inviting visitors to the Host Institution. I will emphasize the cross-disciplinary perspective of my research and aim both at a general audience and at experts in my field. I am already familiar with this exercise as I have already presented the technical details of my work at several conferences, workshops and specialists' seminar series through Europe and Japan.
I am also experienced at aiming at a general audience of mathematicians and I have recently been invited to give a Colloquium talk on my research in Liverpool.
There I have especially focused on the interactions of geometry and arithmetics in the theory of algebraic cycles. Finally, the cross-disciplinary research undertaken will be disseminated at a graduate level through the master's program in mathematics Part III Tripos at Cambridge by designing graduate courses and setting up essays emphasizing the ubiquity of the theory of algebraic cycles.
- Mathematical Physics.
- Lectures on Algebraic Cycles and Chow Groups.
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- The Role of Technology in Science: Philosophical Perspectives.
- Burt Totaro (Author of Group Cohomology and Algebraic Cycles);
This was a demanding task but I thoroughly enjoyed showing the students how techniques from algebra, algebraic geometry, number theory and homological algebra can be brought together and illuminate each other. This way I am directly responsible for developing the students' ability to identify and analyze patterns, logic and critical thinking skills, ability to see relationships, and problem solving skills.
Statistically, students with a postgraduate degree in the mathematical sciences this includes master's degrees and PhDs have the highest average starting salary among all UK holders of postgraduate degrees, according to Adrian Smith's report One Step Beyond March , p. Thus teaching advanced topics such as my research to master's students makes those students very desirable to employers and feeds in the critical pathway towards economic and societal impact.
Group Cohomology and Algebraic Cycles
Publications The following are buttons which change the sort order, pressing the active button will toggle the sort order Author Name descending press to sort ascending. Achter J On descending cohomology geometrically in Compositio Mathematica.
- Langlands program.
- Transport and Chemical Transformation of Pollutants in the Troposphere: An Overview of the Work of EUROTRAC;
- Running an Agile Software Development Project.
- Applications of Analytical Techniques to the Characterization of Materials: Proceedings of an ACS Division of Industrial and Engineering Chemistry Symposium ... Held in Washington, D.C., August 27-31, 1990?
Vial, C. On the motive of certain hyperKaehler varieties in journal fur die reine und angewandte mathematik. Key Findings Impact Summary Collaboration. Description So far, I have discovered new and surprising geometric properties of hyperKaehler varieties.
HyperKaehler varieties are important objects in geometry that come equipped with a very rich structure which explains their significance. They are somehow closely related to so-called Calabi-Yau varieties, whose importance in theoretical physics and in our understanding of the universe cannot be underestimated. Exploitation Route My findings have contributed to the academic knowledge in the field of algebraic geometry.
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Description My findings in the theory of algebraic cycles on hyperKaehler varieties have sparked new directions of research in pure mathematics. I have initiated a fruitful collaboration with Lie Fu Lyon, France ; we have now three articles accepted for publication. My collaboration with Jeff Achter and Sebastian Casalaina-Martin from the University of Colorado and the Colorado State University has grown deeper: we have proved further results of arithmetic significance concerning algebraic cycles.
Related Group Cohomology and Algebraic Cycles
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