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The heat equation corresponding to Dirac operators; existence and uniqueness; asymptotic expansion of heat kernel; index of a Dirac operator; McKean Singer formula

Deletion channels, introduced by Levenshtein in the 60's, are noisy channels that delete bits from the input. A (binary) k-deletion code of length n is a set C of binary strings of length n capable of correcting k such errors, i.e. satisfying the property that no…

The monodromy conjecture predicts a relationship between the motivic zeta function of a hypersurface V(f), which governs the number of solutions to f = 0 (mod p^n) if f has integer coefficients and p is a sufficiently large prime, and the eigenvalues of the monodromy action on the cohomology of…

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Oort conjectured in 1995 that isogeny classes in the moduli space A_g of principally polarised abelian varieties in characteristic p are Zariski dense in the Newton strata containing them. There is a generalisation of this conjecture to the special fibres of Shimura…

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