题目: THE ECONOMICS OF EVOLUTION: SONS OR DAUGHTERS? 摘要:One of the most commonly asked question when a woman is pregnant is whether the parents know if it is a boy or a girl. In humans you have an (almost) 50% chance of guessing the answer correctly. But why is this? Can you correctly explain why there a...
题目: Academic Skills 摘要: I am going to base my two lectures around Academic Skills Handbook that we've developed for the JSC from ANU materials. My first lecture will talk about how an Australian university is run and the different styles of teaching, and then talking about study skills. The second lect...
题目: Beyond the spherical sup-norm problem 摘要: I will present a power-saving estimate in the restricted sup-norm problem of Maass forms for $\rm{SL}_{2}(\mathbb{Z}[i])$, assuming bounded spectral parameter and increasing dimension of the associated $\rm{SU}_{2}(\mathbb{C})$-type. Joint work with Valent...
题目: Generalizations of Alladi's formula for arithmetical semigroups 摘要: In this talk, we will discuss a general version of Alladi’s formula with Dirichlet convolution holds for arithmetical semigroups satisfying Axiom A or Axiom A^#. As applications, we apply our main results to certain semigroups c...
题目: Beyond the Weyl barrier for GL(2) exponential sums 摘要: In this talk, I will introduce the Bessel delta-method and two new variants of the van der Corput method in 2 dimensions, and I will explain how to go beyond the Weyl barrier 3/2=1.5 for GL(2) exponential sums up to 1.63651.... This is joint wo...
题目: On the Rankin-Selberg problem 摘要: In this talk, I will sketch two proofs of the classical result of Rankin and Selberg (in 1939/1940) on the second moment of Fourier coefficients of a GL(2) automorphic form. The Rankin-Selberg problem is that whether one can break the 3/5 barrier in this error term...
题目: Lang-Trotter conjecture for CM elliptic curves 摘要: For any elliptic curve $E$ over $\mathbf{Q}$ and any non-zero integer $r$, the Lang-Trotter conjecture has predicted the asymptotic behaviours of the number of good primes $p\leqslant x$, denoted by $\pi_{E,r}(x)$, such that the Frobenius trace of...