Mathematics and Statistics
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Mathematics plays a critical role in efforts to understand the nature of the physical universe and in the continuing development of technology. Emphasizing excellence in both research and teaching, the Mathematics & Statistics Department at BU offers a wide range of courses in pure and applied mathematics and statistics at the undergraduate and graduate level. The department has particularly strong groups in dynamical systems and applications, geometry/topology, mathematical physics, number theory, and probability and statistics.
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Department chair: Tasso Kaper
Campus address: 111 Cummington Street
Phone: 6173532560
Fax: 6173538100
Website: www.bu.edu/math/
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Gross fibration, SYZ mirror symmetry, and open GromovWitten invariants for toric CalabiYau orbifolds
(International Press, 2016)Given a toric CalabiYau orbifold X, we define and study a nontoric Lagrangian torus fibration on X, which we call the Gross fibration. We apply the SYZ recipe to a suitable modification of the Gross fibration of X to ... 
Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P 1 a,b,c
This paper gives a new way of constructing Landau–Ginzburg mirrors usingdeformation theory of Lagrangian immersions motivated by the works of Seidel,Strominger –Yau–Zaslow and Fukaya–Oh–Ohta–Ono. Moreover, we construct ... 
Lagrangian Floer potential of orbifold spheres
(201701)For each sphere with three orbifold points, we construct an algorithm to compute the open Gromov–Witten potential, which serves as the quantumcorrected Landau–Ginzburg mirror and is an infinite series in general. This ... 
Open Gromov–Witten invariants, mirror maps, and Seidel representations for toric manifolds
(201706)Let X be a compact toric Kähler manifold with −KX nef. Let L⊂X be a regular fiber of the moment map of the Hamiltonian torus action on X. Fukaya, Oh, Ohta, and Ono defined open Gromov–Witten (GW) invariants of X as virtual ... 
Quaternionic Artin representations of Q
(Cambridge University Press, 201707)Isomorphism classes of dihedral Artin representations of ℚ can be counted asymptotically using Siegel's asymptotic averages of class numbers of binary quadratic forms. Here we consider the analogous problem for quaternionic ... 
Appendix: Ray class characters of bounded order and bounded conductor
(Academic Press, 201704) 
A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series
(200808)We consider a time series X=Xk, k∈ℤ with memory parameter d0∈ℝ. This time series is either stationary or can be made stationary after differencing a finite number of times. We study the “local Whittle wavelet estimator” ... 
Asymptotic properties of Uprocesses under longrange dependence
(INST MATHEMATICAL STATISTICS, 20110601)Let (Xi)i≥1 be a stationary meanzero Gaussian process with covariances $\rho(k)=\mathbb {E}(X_{1}X_{k+1})$ satisfying ρ(0) = 1 and ρ(k) = k−DL(k), where D is in (0, 1), and L is slowly varying at infinity. Consider the ... 
Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and waveletbased estimation
(INT STATISTICAL INST, 20071101)We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures ...