Math Calendar
Abstract: In the 1950s, Erdős developed a method to estimate the average of the divisor function over the values of an integer polynomial. Nair and Tenenbaum later extended this to a substantially general class of arithmetic functions.
In 1993 Heath-Brown used character sums to study the average size of the 2-Selmer group in ty^2=x^3-x.
Combining these approaches, we prove that all exponential moments of the rank of P(t)y^2=x^3-x are bounded.
This is joint work with Peter Koymans and Carlo Pagano.
This talk will touch upon joint work with Luca Battistella, Desmond Coles, Andreas Gross, Inder Kaur, Kevin Kühn, Arne Kuhrs, Margarido Melo, Sam Molcho, Annette Werner, Alejandro Vargas, Filippo Viviani, and Dmitry Zakharov.
This is joint work with Marcelo Alves, Matthias Meiwes and Louis Merlin.
Seminar webpage https://utrechtgeometrycentre.nl/ugc-seminar/
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
| We pick up from the previous talk to define Gromov–Witten invariants. First, we provide a short introduction of Chow groups, the algebraic cousin of (co-)homology, in the case of algebraic varieties. Using the definition of Deligne–Mumford stacks from the previous talk, we construct the Kontsevich (moduli) stack of stable maps on projective algebraic varieties over ℂ using nodal curves. We discuss the virtual fundamental class (without proof) in the Chow group and push it forward along an evaluation map to define Gromov–Witten invariants. These will be rational numbers that, in nice cases, correspond to the number of stable maps that satisfy some property. Finally, we will look at the situation of projective space and explicitly calculate the Gromov–Witten invariants. |
Seminar webpage https://utrechtgeometrycentre.nl/ugc-seminar/
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.