NTS ABSTRACTSpring2025: Difference between revisions
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Chidambaram3 (talk | contribs) (Created page with "== Jan 30 == <center> {| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" |- | bgcolor="#F0A0A0" align="center" style="font-size:125%" | |- | bgcolor="#BCD2EE" align="center" | |- | bgcolor="#BCD2EE" | |} </center> <br> == Jan 30 == <center> {| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"...") |
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Back to the number theory seminar main webpage: [https://www.math.wisc.edu/wiki/index.php/NTS Main page] | |||
== Jan 30 == | == Jan 30 == | ||
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" | {| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" | ||
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | | | bgcolor="#F0A0A0" align="center" style="font-size:125%" | L-values and the Mahler measures of polynomials | ||
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| bgcolor="#BCD2EE" align="center" | | | bgcolor="#BCD2EE" align="center" | Xuejun Guo (Nanjing University) | ||
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| bgcolor="#BCD2EE" | | | bgcolor="#BCD2EE" | When the zero locus of a tempered polynomial f(x,y) defines an elliptic curve E, the value L(E,2) is related to the Mahler measure of f(x,y). In this talk, we will explore explicit identities that connect these L-values with Mahler measures for several families of polynomials. | ||
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" | {| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" | ||
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | | | bgcolor="#F0A0A0" align="center" style="font-size:125%" | A new proof of the arithmetic Siegel-Weil formula | ||
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| bgcolor="#BCD2EE" align="center" | | | bgcolor="#BCD2EE" align="center" | Joey Yu Luo (UW-Madison) | ||
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| bgcolor="#BCD2EE" | | | bgcolor="#BCD2EE" | The arithmetic Siegel-Weil formula establishes a profound connection between intersection numbers in Shimura varieties and the Fourier coefficients of central derivatives of Eisenstein series. This result was proven by C. Li and W. Zhang in 2021 using local methods. In this talk, I will present a new proof of the formula that uses the local-global compatibility and the modularity of generating series of special divisors. | ||
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Revision as of 15:09, 14 January 2025
Back to the number theory seminar main webpage: Main page
Jan 30
| L-values and the Mahler measures of polynomials |
| Xuejun Guo (Nanjing University) |
| When the zero locus of a tempered polynomial f(x,y) defines an elliptic curve E, the value L(E,2) is related to the Mahler measure of f(x,y). In this talk, we will explore explicit identities that connect these L-values with Mahler measures for several families of polynomials. |
Feb 6
Feb 13
| A new proof of the arithmetic Siegel-Weil formula |
| Joey Yu Luo (UW-Madison) |
| The arithmetic Siegel-Weil formula establishes a profound connection between intersection numbers in Shimura varieties and the Fourier coefficients of central derivatives of Eisenstein series. This result was proven by C. Li and W. Zhang in 2021 using local methods. In this talk, I will present a new proof of the formula that uses the local-global compatibility and the modularity of generating series of special divisors. |
Feb 20
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