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-~~META:TITLE=Fall 2014 to Spring 2025~~+~~META:TITLE=Fall 2014 to Fall 2025~~ 
 + 
 +--------- 
 + 
 + 
 + 
 + 
 + 
 +---- 
 + 
 +====Fall 2025====
  
    
 +
 + 
 +* **August 20th, Wednesday ** (4:00-5:00pm)\\  \\   
 +**//Speaker //**:  \\      
 +**//Topic//**: organizational meeting  \\     \\  
 +\\ \\ 
 +
 +
 +
 + * **September 10th, Wednesday ** (4:00-5:00pm)\\  \\  
 +**// Speaker //**:  Rohan Sarkar(Binghamton)\\      
 +**//Topic//**: Spectrum of Lévy-Ornstein-Uhlenbeck semigroups on $R^d$   
 +\\ \\  
 +<WRAP box 80%> 
 +**//Abstract//**: We investigate spectral properties of Markov semigroups associated with Ornstein-Uhlenbeck (OU) processes driven by Lévy processes. These semigroups are generated by non-local, non-self-adjoint operators. In the special case where the driving Lévy process is Brownian motion, one recovers the classical diffusion OU semigroup,
 +whose spectral properties have been extensively studied over past few decades. Our main results show that, under suitable conditions on the Lévy process, the spectrum of the Lévy-OU semigroup in the $L^p$-space weighted with the invariant distribution coincides with that of the diffusion OU semigroup. Furthermore, when the drift matrix $B$ is diagonalizable with real eigenvalues, we derive explicit formulas for eigenfunctions and co-eigenfunctions. A key ingredient in our approach is intertwining relationship: we prove that every Lévy-OU semigroup is intertwined with a diffusion OU semigroup, thereby preserving the spectral properties.   
 +
 + \\
 +</WRAP>     
 +\\ \\ 
 +
 +
 + * **September 17th, Wednesday ** (4:00-5:00pm)\\  \\   
 +**//Speaker //**: Ziyao Xu (Binghamton)  \\      
 +**//Topic//**: A Conservative and Positivity-Preserving Discontinuous Galerkin Method for the Population Balance Equation
 +\\ \\  
 +<WRAP box 80%> 
 +**//Abstract//**:  We develop a conservative, positivity-preserving discontinuous Galerkin (DG) method for the population balance equation (PBE), which models the distribution of particle numbers across particle sizes due to growth, nucleation, aggregation, and breakage. To ensure number conservation in growth and mass conservation in aggregation and breakage, we design a DG scheme that applies standard treatment for growth and nucleation, and introduces a novel discretization for aggregation and breakage. The birth and death terms are discretized in a symmetric double-integral form, evaluated using a common refinement of the integration domain and carefully selected quadrature rules. Beyond conservation, we focus on preserving the positivity of the number density in aggregation-breakage. Since local mass corresponds to the first moment, the classical Zhang-Shu limiter, which preserves the zeroth moment (cell average), is not directly applicable. We address this by proving the positivity of the first moment on each cell and constructing a moment-conserving limiter that enforces nonnegativity across the domain. To our knowledge, this is the first work to develop a positivity-preserving algorithm that conserves a prescribed moment. Numerical results verify the accuracy, conservation, and robustness of the proposed method.
 + \\
 +</WRAP>
 +\\ \\ 
 +
 +
 +
 + * **September 24th, Wednesday ** (4:00-5:00pm)(Rosh Hashanah)\\  \\  
 +**// Speaker //**: Rosh Hashanah break \\      
 +**//Topic//**:   
 +\\ \\  
 + 
 +
 +* **October 1st, Wednesday ** (4:00-5:00pm)  (Yom Kippur)\\  \\   
 +**//Speaker//**: Yom Kippur break  \\      
 +**//Topic//**:   
 +\\     \\  
 + 
 +
 +
 +
 + * **October 8th, Wednesday ** (4:00-5:00pm)\\  \\   
 +**//Speaker//**: Prof. Lixin Shen (Syracuse University)  \\ \\     
 +**//Topic//**: Explicit Characterization of the $\ell_p$ Proximity Operator for $0<p<1$  
 +\\     \\
 +<WRAP box 80%> 
 +**//Abstract//**:  The nonconvex $\ell_p$ quasi-norm with $0<p<1$ is a powerful surrogate for sparsity but complicates the evaluation of proximal maps that underpin modern algorithms. In this talk we give an explicit characterization of the scalar proximal operator of $|\cdot|^p$ for all $0<p<1$, including the structure and admissible ranges of global minimizers and conditions ensuring strict, isolated solutions. By applying the Lagrange–Bürmann inversion formula to the stationarity equation, we derive a uniformly convergent series for the larger positive root, yielding an exact and numerically stable formula for the $\ell_p$ proximal map above the classical threshold. We further provide a Mellin–Barnes integral representation and identify the series as a Fox–Wright function, which determines its radius of convergence. Specializations recover the known closed forms for $p=\tfrac12$ and $p=\tfrac23$, and we supply compact hypergeometric expressions for additional rational cases (e.g., $p=\tfrac13$). These results unify scattered formulas into a single framework and enable high-accuracy evaluation of $\ell_p$ proximity operators across the full range $0<p<1$.
 +
 +
 +\\
 +</WRAP>     
 +\\ \\ 
 +
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 +
 +* **October 30th, Thursday(Special date) ** (4:00-5:00pm) \\  \\   
 +**//Speaker//**: Zengyan Zhang (Penn State) \\      
 +**//Topic//**: Geometric local parameterization for solving Hele-Shaw problems with surface tension 
 + 
 +\\     \\  
 +<WRAP box 80%> 
 +**//Abstract//**: With broad applications in biology, physics, and material science, including tumor growth and fluid interface dynamics, the Hele-Shaw problem with surface tension provides a canonical model for studying the dynamics of evolving interfaces. Solving such problems requires precise treatment of sharp boundaries. However, constructing a global parameterization for complicated surfaces and explicitly tracking boundary motion is challenging. In this work, we present a geometric local parameterization approach for efficiently solving the two-dimensional Hele-Shaw problems, where the boundary is identified only from randomly sampled data. Through convergence and error analysis, as well as numerical experiments, we demonstrate the capability and effectiveness of our approach in resolving complex interface evolution.
 +
 +</WRAP>
 +\\ \\ 
 +
 +
 +
 + **November 5th, Wednesday ** (4:00-5:00pm)  \\  \\   
 +**//Speaker//**: Yuanyuan Pan (Syracuse University) \\      
 +**//Topic//**: On the Spectral Geometry and Small-Time Mass of Anderson Models on Planar Domains
 +
 +\\     \\  
 +<WRAP box 80%> 
 +**//Abstract//**: We consider the Anderson Hamiltonian (AH) and the parabolic Anderson model (PAM) with white noise and Dirichlet boundary condition on a bounded planar domain $D\subset\mathbb R^2$. We compute the small-$t$ asymptotics of the AH's exponential trace up to order $O(\log t)$, and of the PAM's mass up to order $O(t\log t)$.
 +Applications of our main result include the following:
 +
 +(i) If the boundary $\partial D$ is sufficiently regular, then $D$'s area and $\partial D$'s length can both be recovered almost surely from a single observation of the AH's eigenvalues.
 +
 +(ii) If $D$ is simply connected and $\partial D$ is fractal, then $\partial D$'s Minkowski dimension (if it exists)
 +can be recovered almost surely from the PAM's small-$t$ asymptotics.
 +
 +(iii) The variance of the white noise can be recovered almost surely from a single observation of the AH's eigenvalues.
 +  
 + \\
 +</WRAP>
 +\\ \\ 
 +
 +
 +
 +
 +
 + * **Room 309, November 20th, Thursday ** (4:00-5:00pm) (Special room and time)\\  \\   
 +**//Speaker//**:   Brian Kirby(Binghamton University)\\      
 +**//Topic//**: Compactifying the Manifold given by the Schwartzchild Metric
 +\\     \\  
 +<WRAP box 80%> 
 +**//Abstract//**: Consider the metric in $\mathbb{R}^4$ given by $ds^2=f(r)dt^2 − 1/f(r)dr^2 − r^2dg^2$, where $g$ is the standard Riemannian metric in $\mathbb{R}^2$, $f(r) = \phi(r)(r − r_0)$, where $\phi$ is a continuous, differentiable, positive function on $\mathbb{R}$. We will construct the Penrose diagram (the compactified manifold) for the given metric via coordinate changes and compactification. We will then discuss extensions to topological Penrose Diagrams and metric functions with an arbitrary number of roots, if time permits.
 + \\
 +</WRAP>
 +\\ \\ 
 +
 +
 +* **November 26th, Wednesday ** (4:00-5:00pm) (Thanksgiving Break)\\  \\   
 +**//Speaker//**:  Thanksgiving Break  \\      
 +**//Topic//**:  
 +\\     \\  
 +
 +
 +
 +
 +
 +* **December 3rd, Wednesday ** (4:00-5:00pm)\\  \\   
 +**//Speaker//**:  Job interview  \\      
 +**//Topic//**:  
 +\\     \\  
 +<WRAP box 80%> **//Abstract//**: 
 +
 +
 + \\
 +</WRAP>
 +\\ \\ 
 +
 + 
 +
 +
 ---- ----
  
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-* **August 28th, Wednesday ** (3:30-4:30pm)\\  \\    
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- * **September 4th, Wednesday ** (3:30-4:30pm)\\  \\    
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 * **October 2nd , Wednesday ** (3:30-4:30pm) (Rosh Hashanah and Fall Break)\\  \\    * **October 2nd , Wednesday ** (3:30-4:30pm) (Rosh Hashanah and Fall Break)\\  \\   
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- * **October 9th, Wednesday ** (3:30-4:30pm)\\  \\    
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-* **October 16th, Wednesday ** (3:30-4:30pm) \\  \\    
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- **November 6th, Wednesday ** (3:30-4:30pm)  \\  \\    
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- * **November 20th, Wednesday ** (3:30-4:55pm) \\  \\    
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- * **January 31st, Wednesday ** (4-5pm)\\   
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- * **March 6th, Wednesday ** (4-5pm) **(Spring Break)**\\  \\   **//Speaker//**:  \\      **//Topic//**:   + * **March 6th, Wednesday ** (4-5pm) **(Spring Break)**\\   
 +\\   **//Speaker//**:  \\     
 +  **//Topic//**:   
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-* **March 27th, Wednesday ** (4-5pm) \\  \\    
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-* **April 3rd, Wednesday ** (4-5pm) \\  \\   
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-* **May 8th, Wednesday ** (4-5pm) \\  \\   
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- * **September 6th, Wednesday ** (3:30-4:30pm)\\  \\    
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-**//Topic//**:  No talk this week 
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 * **October 4th , Wednesday ** (3:30-4:30pm)\\  \\    * **October 4th , Wednesday ** (3:30-4:30pm)\\  \\   
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- * **October 11th, Wednesday ** (3:30-4:30pm)\\  \\    
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-* **October 25th, Wednesday ** (3:30-4:30pm) \\  \\    
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-* **November 29th, Wednesday ** (3:30-4:30pm)\\  \\    
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-* **December 6th, Wednesday ** (3:30-4:30pm)\\  \\    
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- * **February 1st, Wednesday ** (3:30-4:30pm)\\   
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-* **February 15th , Wednesday ** (3:30-4:30pm) \\   
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-* **March 2nd, Thursday ** (3:30-4:30pm) \\  \\   **//Speaker//**: Jacob Shapiro (Princeton)  \\      +* **March 2nd, Thursday ** (3:30-4:30pm) \\  \\   
 + **//Speaker//**: Jacob Shapiro (Princeton)  \\      
 **//Topic//**:   The Classification Problem of Disordered Topological Insulators **//Topic//**:   The Classification Problem of Disordered Topological Insulators
 \\     \\   \\     \\  
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- * **March 8th, Wednesday ** (3:30-4:30pm) \\  \\   **//Speaker//**:  \\      **//Topic//**:    
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-</WRAP> 
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-* **March 15th, Wednesday ** (3:30-4:30pm) \\  \\   **//Speaker//**:    \\      **//Topic//**:    
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- * **March 22nd, Wednesday ** (3:30-4:30pm) \\  \\   **//Speaker//**: Mihai Stoiciu (Williams College) \\      **//Topic//**: The Eigenvalue Distribution for Random Unitary Matrices: An Approach Using Entropy + * **March 22nd, Wednesday ** (3:30-4:30pm) \\   
 +\\   **//Speaker//**: Mihai Stoiciu (Williams College)  
 +\\  **//Topic//**: The Eigenvalue Distribution for Random Unitary Matrices: An Approach Using Entropy 
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**: CMV matrices are the unitary analogues of one-dimensional discrete Schrodinger operators. Depending on the distribution of their coefficients, random CMV matrices exhibit a transition in their eigenvalue distribution from a Poisson process (no eigenvalue correlation) to "picket fence" (strong eigenvalue repulsion). We investigate this transition from the perspective of the joint entropy of the coefficients of the random CMV matrix. <WRAP box 80%> **//Abstract//**: CMV matrices are the unitary analogues of one-dimensional discrete Schrodinger operators. Depending on the distribution of their coefficients, random CMV matrices exhibit a transition in their eigenvalue distribution from a Poisson process (no eigenvalue correlation) to "picket fence" (strong eigenvalue repulsion). We investigate this transition from the perspective of the joint entropy of the coefficients of the random CMV matrix.
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-* **March 29th, Wednesday ** (3:30-4:30pm) \\  \\   **//Speaker//**: David Renfrew (Binghamton University)   \\      **//Topic//**:    Eigenvalues of minors of random matrices and roots of derivatives of random polynomials+* **March 29th, Wednesday ** (3:30-4:30pm) \\   
 +\\   **//Speaker//**: David Renfrew (Binghamton University)    
 +\\   **//Topic//**:    Eigenvalues of minors of random matrices and roots of derivatives of random polynomials
  
  
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-* **April 5th, Wednesday ** (3:30-4:30pm) **(Spring break) **\\  \\   **//Speaker//**:   \\      **//Topic//**:    +* **April 5th, Wednesday ** (3:30-4:30pm) **(Spring break) **\\   
 +\\   **//Speaker//**:    
 +\\      **//Topic//**:    
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:    <WRAP box 80%> **//Abstract//**:   
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- * **April 12th, Wednesday ** (3:30-4:30pm)  \\  \\   **//Speaker//**:Rongwei Yang (University at Albany)  \\      **//Topic//**:  Joint spectrum and the Julia set+ * **April 12th, Wednesday ** (3:30-4:30pm)  \\   
 +\\   **//Speaker//**:Rongwei Yang (University at Albany)   
 +\\   **//Topic//**:  Joint spectrum and the Julia set
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:   It was discovered recently that the joint spectrum of linear operators gives rise to an interesting link between self-similar group representations and complex dynamics. This talk will review this link. In particular, we shall see that, in the case of the infinite dihedral group $D_\infty$, the projective joint spectrum coincides with the Julia set of of a rational map on the projective space ${\mathbb P}^2$ derived from the self-similarity. Such connection also seems to exist for some more complicated groups, such as the lamplighter group and the group of intermediate growth. <WRAP box 80%> **//Abstract//**:   It was discovered recently that the joint spectrum of linear operators gives rise to an interesting link between self-similar group representations and complex dynamics. This talk will review this link. In particular, we shall see that, in the case of the infinite dihedral group $D_\infty$, the projective joint spectrum coincides with the Julia set of of a rational map on the projective space ${\mathbb P}^2$ derived from the self-similarity. Such connection also seems to exist for some more complicated groups, such as the lamplighter group and the group of intermediate growth.
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-* **April 19th, Wednesday ** (3:30-4:30pm) \\  \\   **//Speaker//**:     \\      **//Topic//**:   
-\\     \\   
-<WRAP box 80%> **//Abstract//**:  
-  
- \\ 
-</WRAP> 
-\\ \\  
- 
- 
- * **April 26th, Wednesday ** (3:30-4:30pm) \\  \\   **//Speaker//**:  Paul Barber (Binghamton)  \\      **//Topic//**:    
-\\     \\   
-<WRAP box 80%> **//Abstract//**:   
- 
- \\ 
-</WRAP> 
-\\ \\  
  
  
  
-* **May 3rd, Wednesday ** (3:30-4:30pm) \\  \\   **//Speaker//**:   \\      **//Topic//**:   
  
 + * **April 26th, Wednesday ** (3:30-4:30pm) \\  
 +\\   **//Speaker//**:  Paul Barber (Binghamton)  
 +\\      **//Topic//**:   
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:   <WRAP box 80%> **//Abstract//**:  
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- 
-* **November 16th, Wednesday ** (3:30-4:30pm)\\  \\    
-**//Speaker//**:    \\       
-**//Topic//**:   
-\\     \\   
-<WRAP box 80%> **//Abstract//**:  
- 
- \\ 
-</WRAP> 
-\\ \\  
  
  
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 \\ \\  \\ \\ 
  
- 
-* **November 30th, Wednesday ** (3:30-4:30pm)\\  \\    
-**//Speaker//**:    \\       
-**//Topic//**:   
-\\     \\   
-<WRAP box 80%> **//Abstract//**:  
- 
- \\ 
-</WRAP> 
-\\ \\  
- 
- 
- 
- 
-* **December 7th, Wednesday ** (3:30-4:30pm)\\  \\    
-**//Speaker//**:    \\       
-**//Topic//**:   
-\\     \\   
-<WRAP box 80%> **//Abstract//**:  
- 
- \\ 
-</WRAP> 
-\\ \\  
- 
- \\ 
-</WRAP> 
-\\ \\  
- 
-   
-\\ \\  
  
 ----  ---- 
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 \\ \\  \\ \\ 
  
- * **January 29th, Wednesday ** (4:00-5:00pm)\\  \\   **//Speaker //**:  organizational meeting  \\      **//Topic//**:   organizational meeting + * **January 29th, Wednesday ** (4:00-5:00pm)\\   
 +\\   **//Speaker //**:  organizational meeting   
 +\\      **//Topic//**:   organizational meeting 
 \\ \\   \\ \\  
 <WRAP box 80%> **//Abstract//**:   organizational meeting  <WRAP box 80%> **//Abstract//**:   organizational meeting 
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- * **February 5th, Wednesday ** (4:00-5:00pm)\\  \\   **//Speaker //**: David Renfrew (Binghamton) \\      **//Topic//**: The circular law+ * **February 5th, Wednesday ** (4:00-5:00pm)\\   
 +\\   **//Speaker //**: David Renfrew (Binghamton)  
 +\\      **//Topic//**: The circular law
 \\ \\   \\ \\  
 <WRAP box 80%> **//Abstract//**: I will discuss the eigenvalues of random matrices with i.i.d. entries and show they converge to the uniform measure on the unit disk. <WRAP box 80%> **//Abstract//**: I will discuss the eigenvalues of random matrices with i.i.d. entries and show they converge to the uniform measure on the unit disk.
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- * **February 12th, Wednesday ** (3:30-4:30pm)\\  \\  **// Speaker //**: Guillaume Dubach (CUNY Baruch) \\      **//Topic//**:  Words and surfaces + * **February 12th, Wednesday ** (3:30-4:30pm)\\   
 +\\  **// Speaker //**: Guillaume Dubach (CUNY Baruch)  
 +\\      **//Topic//**:  Words and surfaces 
 \\ \\   \\ \\  
 <WRAP box 80%> **//Abstract//**: Words of random matrices with i.i.d. complex Gaussian entries (a.k.a. complex Ginibre matrices) can be studied using a topological expansion formula, or genus expansion. This results in a generalization of well-known properties of products of i.i.d. complex Ginibre matrices on the one hand, and powers of one Ginibre matrix on the other hand. For instance, the empirical distribution of singular values of any word is shown to converge to a Fuss-Catalan distribution whose parameter only depends on the length of the word. (Joint work with Yuval Peled.) <WRAP box 80%> **//Abstract//**: Words of random matrices with i.i.d. complex Gaussian entries (a.k.a. complex Ginibre matrices) can be studied using a topological expansion formula, or genus expansion. This results in a generalization of well-known properties of products of i.i.d. complex Ginibre matrices on the one hand, and powers of one Ginibre matrix on the other hand. For instance, the empirical distribution of singular values of any word is shown to converge to a Fuss-Catalan distribution whose parameter only depends on the length of the word. (Joint work with Yuval Peled.)
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-* **February 19th , Wednesday ** (3:40-4:40pm) \\  \\   **//Speaker//**:  Indrajit Jana (Temple University) \\      **//Topic//**:  CLT for non-Hermitian random band matrices with variance profiles.+* **February 19th , Wednesday ** (3:40-4:40pm) \\   
 +\\   **//Speaker//**:  Indrajit Jana (Temple University)  
 +\\      **//Topic//**:  CLT for non-Hermitian random band matrices with variance profiles.
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:  We show that the fluctuations of the linear eigenvalue statistics of a non-Hermitian random band matrix of bandwidth $b_{n}$ with a continuous variance profile converges to a Gaussian distribution. We obtain an explicit formula for the variance of the limiting Gaussian distribution, which depends on the test function, and as well as the growth rate of the bandwidth $b_{n}$. In particular, if the band matrix is a full matrix i.e., $b_{n}=n$, the formula is consistent with Rider, and Silverstein (2006). We also compute an explicit formula for the limiting variance even if the bandwidth $b_{n}$ grows at a slower rate compared to $n$ i.e., $b_{n}=o(n)$. <WRAP box 80%> **//Abstract//**:  We show that the fluctuations of the linear eigenvalue statistics of a non-Hermitian random band matrix of bandwidth $b_{n}$ with a continuous variance profile converges to a Gaussian distribution. We obtain an explicit formula for the variance of the limiting Gaussian distribution, which depends on the test function, and as well as the growth rate of the bandwidth $b_{n}$. In particular, if the band matrix is a full matrix i.e., $b_{n}=n$, the formula is consistent with Rider, and Silverstein (2006). We also compute an explicit formula for the limiting variance even if the bandwidth $b_{n}$ grows at a slower rate compared to $n$ i.e., $b_{n}=o(n)$.
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- * ** February 26th , Wednesday ** (4:00-5:00pm) \\  \\   **//Speaker//**: Liming Sun (John Hopkins) \\ \\     **//Topic//**: Some convexity theorems of translating solitons in the mean curvature flow+ * ** February 26th , Wednesday ** (4:00-5:00pm) \\   
 +\\   **//Speaker//**: Liming Sun (John Hopkins) \\  
 +\\     **//Topic//**: Some convexity theorems of translating solitons in the mean curvature flow
 \\     \\ \\     \\
 <WRAP box 80%> **//Abstract//**:I will be talking about the translating solitons (translators) in the mean curvature flow. Convexity theorems of translators play fundamental roles in the classification of them. Spruck and Xiao proved any two dimensional mean convex translator is actually convex. Spruck and I proved a similar convex theorem for higher dimensional translators, namely the 2-convex translating solitons are actually convex. Our theorem implies 2-convex translating solitons have to be the bowl soliton. Our second theorem regards the solutions of the Dirichlet problem for translators in a bounded convex domain . We proved the solutions will be convex under appropriate conditions. This theorem implies the existence of n-2 family of locally strictly convex translators in higher dimension. In the end, we will show that our method could be used to establish a convexity theorem for constant mean curvature graph equation. <WRAP box 80%> **//Abstract//**:I will be talking about the translating solitons (translators) in the mean curvature flow. Convexity theorems of translators play fundamental roles in the classification of them. Spruck and Xiao proved any two dimensional mean convex translator is actually convex. Spruck and I proved a similar convex theorem for higher dimensional translators, namely the 2-convex translating solitons are actually convex. Our theorem implies 2-convex translating solitons have to be the bowl soliton. Our second theorem regards the solutions of the Dirichlet problem for translators in a bounded convex domain . We proved the solutions will be convex under appropriate conditions. This theorem implies the existence of n-2 family of locally strictly convex translators in higher dimension. In the end, we will show that our method could be used to establish a convexity theorem for constant mean curvature graph equation.
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-* **March 4th, Wednesday ** (4:00-5:00pm) **(Winter Break)**\\  \\   **//Speaker//**:  \\      **//Topic//**:   +* **March 4th, Wednesday ** (4:00-5:00pm) **(Winter Break)**\\   
 +\\   **//Speaker//**:   
 +\\      **//Topic//**:   
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:  <WRAP box 80%> **//Abstract//**: 
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 \\ \\  \\ \\ 
  
- 
- 
- 
- * **March 11th, Wednesday ** (4:00-5:00pm) \\  \\   **//Speaker//**:  \\      **//Topic//**:    
-\\     \\   
-<WRAP box 80%> **//Abstract//**:  
- \\ 
-</WRAP> 
-\\ \\  
  
  
  
  
-* **March 18th, Wednesday ** (4:00-5:00pm) \\  \\   **//Speaker//**:  Gang Zhou  \\      **//Topic//**:   +* **March 18th, Wednesday ** (4:00-5:00pm) \\   
 +\\   **//Speaker//**:  Gang Zhou   
 +\\      **//Topic//**:   
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:   <WRAP box 80%> **//Abstract//**:  
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- * **March 25th, Wednesday ** (4:00-5:00pm) \\  \\   **//Speaker//**: Xiangjin Xu  \\      **//Topic//**:  + * **March 25th, Wednesday ** (4:00-5:00pm) \\   
 +\\   **//Speaker//**: Xiangjin Xu   
 +\\      **//Topic//**:  
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:  <WRAP box 80%> **//Abstract//**: 
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-* **April 1st, Wednesday ** (4:00-5:00pm) \\  \\   **//Speaker//**: Paul Barber \\      **//Topic//**:    +* **April 1st, Wednesday ** (4:00-5:00pm) \\   
 +\\   **//Speaker//**: Paul Barber  
 +\\      **//Topic//**:    
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:    <WRAP box 80%> **//Abstract//**:   
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- * **April 8th, Wednesday ** (4:00-5:00pm) **(Spring break) ** \\  \\   **//Speaker//**:  \\      **//Topic//**:  + * **April 8th, Wednesday ** (4:00-5:00pm) **(Spring break) ** \\   
 +\\   **//Speaker//**:   
 +\\      **//Topic//**:  
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:    <WRAP box 80%> **//Abstract//**:   
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- * **April 22nd, Wednesday ** (4:00-5:00pm) \\  \\   **//Speaker//**: Gang's visitor  \\      **//Topic//**:   + * **April 22nd, Wednesday ** (4:00-5:00pm) \\   
 +\\   **//Speaker//**: Gang's visitor   
 +\\      **//Topic//**:   
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:   <WRAP box 80%> **//Abstract//**:  
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 \\ \\  \\ \\ 
  
- 
- 
-* **April 29th, Wednesday ** (4:00-5:00pm) \\  \\   **//Speaker//**:   \\      **//Topic//**:   
- 
-\\     \\   
-<WRAP box 80%> **//Abstract//**:   
- 
- \\ 
-</WRAP> 
-\\ \\  
- 
- 
- 
- 
- * **May 6th, Wednesday ** (4:00-5:00pm) \\  \\   **//Speaker//**:\\      **//Topic//**:   
-\\     \\   
-<WRAP box 80%> **//Abstract//**:   
-W 
- \\ 
-</WRAP> 
-\\ \\  
-   
-\\ \\  
  
 --------- ---------
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-* **August 28th, Wednesday ** (3:30-4:30pm)\\  \\   **//Speaker //**:  \\      **//Topic//**: organizational meeting  \\     \\  +* **August 28th, Wednesday ** (3:30-4:30pm)\\   
 +\\   **//Speaker //**:   
 +\\      **//Topic//**: organizational meeting  \\     \\  
 \\ \\  \\ \\ 
  
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- * **September 5th, Thursday ** (WH 309, 2:30-4:30pm)(Special time and location)\\  \\   **//Speaker //**:  David Cervantes-Nava (Binghamton University) \\      **//Topic//**: Admissions to Candidacy Exam+ * **September 5th, Thursday ** (WH 309, 2:30-4:30pm)(Special time and location)\\   
 +\\   **//Speaker //**:  David Cervantes-Nava (Binghamton University)  
 +\\      **//Topic//**: Admissions to Candidacy Exam
 \\ \\   \\ \\  
 <WRAP box 80%> **//Abstract//**: TBD \\ <WRAP box 80%> **//Abstract//**: TBD \\
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 \\ \\  \\ \\ 
  
- 
- * **September 11th, Wednesday ** (3:30-4:55pm)\\  \\   **//Speaker //**:   \\      **//Topic//**:  
-\\ \\   
-<WRAP box 80%> **//Abstract//**:  
- 
- \\ 
-</WRAP> 
-\\ \\  
  
  
  
- * **September 18th, Wednesday ** (4:00-5:00pm)\\  \\  **// Speaker //**: Xiangjin Xu (Binghamton University) \\      **//Topic//**:  Characterization of Carleson measures on compact manifolds with boundary + * **September 18th, Wednesday ** (4:00-5:00pm)\\   
 +\\  **// Speaker //**: Xiangjin Xu (Binghamton University)  
 +\\      **//Topic//**:  Characterization of Carleson measures on compact manifolds with boundary 
 \\ \\   \\ \\  
 <WRAP box 80%> **//Abstract//**:  On the subspaces of $L^2(M)$ generated by eigenfunctions of eigenvalues less than $L(>1)$ associated to the Dirichlet (Neumann) Laplace–Beltrami operator on a compact Riemannian manifold $(M,g)$ with boundary,  we discuss some positive and negative results on the characterization of the Carleson measures and the Logvinenko–Sereda sets for Dirichlet (or Neumann) Laplacian on $M$, which generalized the corresponding results of J. Ortega-Cerda and B. Pridhnani on a compact boundaryless manifold (Forum Math.25 (2013), DOI 10.1515/FORM.2011.110). <WRAP box 80%> **//Abstract//**:  On the subspaces of $L^2(M)$ generated by eigenfunctions of eigenvalues less than $L(>1)$ associated to the Dirichlet (Neumann) Laplace–Beltrami operator on a compact Riemannian manifold $(M,g)$ with boundary,  we discuss some positive and negative results on the characterization of the Carleson measures and the Logvinenko–Sereda sets for Dirichlet (or Neumann) Laplacian on $M$, which generalized the corresponding results of J. Ortega-Cerda and B. Pridhnani on a compact boundaryless manifold (Forum Math.25 (2013), DOI 10.1515/FORM.2011.110).
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-* **September 25th , Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**: Gang Zhou (Binghamton University)  \\      **//Topic//**: The dynamics of effective equation of polaron +* **September 25th , Wednesday ** (3:30-4:55pm) \\   
 +\\   **//Speaker//**: Gang Zhou (Binghamton University)   
 +\\      **//Topic//**: The dynamics of effective equation of polaron 
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**: Polaron theory is a model of an electron in a crystal lattice. It is studied in the framework of nonequilibrium statistic mechanics, and it has a lot of applications. In the recent year, jointly with Rupert Frank, we studied the quantum and classical models and obtained different results. Still there are open problems. In this talk I present the results for the dynamics of classical model.  <WRAP box 80%> **//Abstract//**: Polaron theory is a model of an electron in a crystal lattice. It is studied in the framework of nonequilibrium statistic mechanics, and it has a lot of applications. In the recent year, jointly with Rupert Frank, we studied the quantum and classical models and obtained different results. Still there are open problems. In this talk I present the results for the dynamics of classical model. 
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- 
- * **October 2nd, Wednesday ** (3:30-4:55pm)\\  \\   **//Speaker//**:  \\ \\     **//Topic//**:   
-\\     \\ 
-<WRAP box 80%> **//Abstract//**: 
- 
-\\ 
-</WRAP>      
-\\ \\  
  
  
    
  
-* **October 9th, Wednesday ** (3:30-4:55pm)(Holiday, Yom Kippur) \\  \\   **//Speaker//**:  \\      **//Topic//**:   +* **October 9th, Wednesday ** (3:30-4:55pm)(Holiday, Yom Kippur) \\   
 +\\   **//Speaker//**:   
 +\\      **//Topic//**:   
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:  <WRAP box 80%> **//Abstract//**: 
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- * **October 17th, Thursday ** (1:00-2:00pm, WH 309) Note the special time and location\\  \\   **//Speaker//**: Yuan Yuan, Syracuse University \\      **//Topic//**: Bergman projection on pseudoconvex domains+ * **October 17th, Thursday ** (1:00-2:00pm, WH 309) Note the special time and location\\   
 +\\   **//Speaker//**: Yuan Yuan, Syracuse University  
 +\\      **//Topic//**: Bergman projection on pseudoconvex domains
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**: Bergman projection plays important roles in function theory and d-bar Neumann problem on pseudoconvex domains. After giving a brief introduction to the general theory, I will focus on the boundedness of the Bergman projection in L^p spaces. This talk is based on joint work with Chen and Krantz. <WRAP box 80%> **//Abstract//**: Bergman projection plays important roles in function theory and d-bar Neumann problem on pseudoconvex domains. After giving a brief introduction to the general theory, I will focus on the boundedness of the Bergman projection in L^p spaces. This talk is based on joint work with Chen and Krantz.
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-* **October 23rd, Wednesday ** (4:00-5:00pm) \\  \\   **//Speaker//**:  Adam Weisblatt (Binghamton University) \\      **//Topic//**: The wraparound universe+* **October 23rd, Wednesday ** (4:00-5:00pm) \\   
 +\\   **//Speaker//**:  Adam Weisblatt (Binghamton University)  
 +\\      **//Topic//**: The wraparound universe
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**: Cosmologists have been trying to determine the shape of the universe. <WRAP box 80%> **//Abstract//**: Cosmologists have been trying to determine the shape of the universe.
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- * **October 30th, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**:  \\      **//Topic//**:   
-\\     \\   
-<WRAP box 80%> **//Abstract//**:\\ 
-</WRAP> 
-\\ \\  
  
  
- +* **November 6th, Wednesday ** (4:00-5:00pm) \\   
- +\\   **//Speaker//**: Alexis Drouot, Columbia University  
-* **November 6th, Wednesday ** (4:00-5:00pm) \\  \\   **//Speaker//**: Alexis Drouot, Columbia University \\      **//Topic//**:    Transport at interfaces of topological insulators+\\      **//Topic//**:    Transport at interfaces of topological insulators
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:   In this talk, I consider a PDE modeling interface effects between  insulators: a Schrodinger equation with periodic asymptotics (the  bulk), away from a strip (the interface). I will state the bulk-edge  correspondence. This theorem predicts that the interface between two  topologically distinct insulators always conducts energy. I will  illustrate it in the context of graphene;  explain applications to  robust waveguides; and provide dynamical interpretations. <WRAP box 80%> **//Abstract//**:   In this talk, I consider a PDE modeling interface effects between  insulators: a Schrodinger equation with periodic asymptotics (the  bulk), away from a strip (the interface). I will state the bulk-edge  correspondence. This theorem predicts that the interface between two  topologically distinct insulators always conducts energy. I will  illustrate it in the context of graphene;  explain applications to  robust waveguides; and provide dynamical interpretations.
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- * **November 13th, Wednesday ** (4:00-5:00pm)  \\  \\   **//Speaker//**: Steven Gindi (Binghamton University)\\      **//Topic//**:  Long Time Limits of Generalized Ricci Flow+ * **November 13th, Wednesday ** (4:00-5:00pm)  \\   
 +\\   **//Speaker//**: Steven Gindi (Binghamton University) 
 +\\      **//Topic//**:  Long Time Limits of Generalized Ricci Flow
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:  We derive modified Perelman-type monotonicity formulas for solutions to the generalized Ricci flow equation with symmetry on principal bundles. This leads to rigidity and classification results for nonsingular solutions.  <WRAP box 80%> **//Abstract//**:  We derive modified Perelman-type monotonicity formulas for solutions to the generalized Ricci flow equation with symmetry on principal bundles. This leads to rigidity and classification results for nonsingular solutions. 
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-* **November 20th, Wednesday ** (3:30-4:55pm)\\  \\   **//Speaker//**:    \\      **//Topic//**:   + * **November 27th, Wednesday ** (3:30-4:55pm)(Thanksgiving break) \\   
-\\     \\   +\\   **//Speaker//**:    
-<WRAP box 80%> **//Abstract//**:  +\\      **//Topic//**:  
- +
- \\ +
-</WRAP> +
-\\ \\  +
- +
- +
- * **November 27th, Wednesday ** (3:30-4:55pm)(Thanksgiving break) \\  \\   **//Speaker//**:   \\      **//Topic//**:  +
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**: <WRAP box 80%> **//Abstract//**:
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- * **January 23rd, Wednesday ** (3:30-4:30pm)\\  \\   **//Speaker //**:  \\      **//Topic//**: organizational meeting  \\     \\  + * **January 23rd, Wednesday ** (3:30-4:30pm)\\   
 +\\   **//Speaker //**:   
 +\\      **//Topic//**: organizational meeting  \\     \\  
 \\ \\  \\ \\ 
  
- * **January 30th, Wednesday ** (3:30-5:00pm)(No talk due Monday schedule)\\  \\   **//Speaker //**:   \\      **//Topic//**:   No talk + * **January 30th, Wednesday ** (3:30-5:00pm)(No talk due Monday schedule)\\   
 +\\   **//Speaker //**:    
 +\\      **//Topic//**:   No talk 
 \\ \\   \\ \\  
 <WRAP box 80%> **//Abstract//**:    <WRAP box 80%> **//Abstract//**:   
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- 
- * **February 6th, Wednesday ** (3:30-4:55pm)\\  \\   **//Speaker //**:  \\      **//Topic//**:  
-\\ \\   
-<WRAP box 80%> **//Abstract//**:  
- 
- \\ 
-</WRAP> 
-\\ \\  
- 
- 
- 
- * **February 13th, Wednesday ** (3:30-4:55pm)\\  \\  **// Speaker //**:  \\      **//Topic//**:    
-\\ \\   
-<WRAP box 80%> **//Abstract//**:  
- \\ 
-</WRAP>      
-\\ \\  
- 
- 
- 
-* **February 20th , Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**:   \\      **//Topic//**:   
-\\     \\   
-<WRAP box 80%> **//Abstract//**:   
- 
- 
- 
- \\ 
-</WRAP> 
-\\ \\  
- 
- 
- 
- * ** February 27th , Wednesday ** (3:30-4:55pm)\\  \\   **//Speaker//**:  \\ \\     **//Topic//**: 
-\\     \\ 
-<WRAP box 80%> **//Abstract//**: 
- 
-\\ 
-</WRAP>      
-\\ \\  
- 
- 
-  
- 
-* **March 6th, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**:  \\      **//Topic//**:    
-\\     \\   
-<WRAP box 80%> **//Abstract//**:  
- 
- \\ 
-</WRAP> 
-\\ \\  
- 
- 
- 
- 
- * **March 13th, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**:  \\      **//Topic//**:    
-\\     \\   
-<WRAP box 80%> **//Abstract//**:  
- \\ 
-</WRAP> 
-\\ \\  
- 
- 
- 
- 
-* **March 20th, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**:    \\      **//Topic//**:    
-\\     \\   
-<WRAP box 80%> **//Abstract//**:   
- 
- \\ 
-</WRAP> 
-\\ \\  
- 
- 
- 
- 
- * **March 27th, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**:   \\      **//Topic//**:   
-\\     \\   
-<WRAP box 80%> **//Abstract//**:  
- 
- \\ 
-</WRAP> 
-\\ \\  
- 
- 
- 
- 
-* **April 3rd, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**: \\      **//Topic//**:     
-\\     \\   
-<WRAP box 80%> **//Abstract//**:    
- 
-</WRAP> 
-\\ \\  
- 
- 
- 
- * **April 10th, Wednesday ** (3:30-4:55pm)  \\  \\   **//Speaker//**:  \\      **//Topic//**:   
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-<WRAP box 80%> **//Abstract//**:    
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-</WRAP> 
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-* **April 17th, Wednesday ** (3:30-4:55pm)\\  \\   **//Speaker//**:     \\      **//Topic//**:   
-\\     \\   
-<WRAP box 80%> **//Abstract//**:  
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-</WRAP> 
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- * **April 24th, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**:   \\      **//Topic//**:    
-\\     \\   
-<WRAP box 80%> **//Abstract//**:   
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-</WRAP> 
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-* **May 1st, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**:  Lu Wang  (University of Wisconsin & IAS) \\      **//Topic//**:  Mean Curvature Flow Expanders of Low Entropy +* **May 1st, Wednesday ** (3:30-4:55pm) \\   
 +\\   **//Speaker//**:  Lu Wang  (University of Wisconsin & IAS)  
 +\\      **//Topic//**:  Mean Curvature Flow Expanders of Low Entropy 
  
 \\     \\   \\     \\  
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- * **May 8th, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**:John Ma (Rutgers University)\\      **//Topic//**:   Uniqueness Theorem for non-compact Mean Curvature Flow with possibly unbounded curvatures+ * **May 8th, Wednesday ** (3:30-4:55pm) \\   
 +\\   **//Speaker//**:John Ma (Rutgers University) 
 +\\      **//Topic//**:   Uniqueness Theorem for non-compact Mean Curvature Flow with possibly unbounded curvatures
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:   <WRAP box 80%> **//Abstract//**:  
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- * **May 15th, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**:   \\      **//Topic//**:    
-\\     \\   
-<WRAP box 80%> **//Abstract//**:   
  
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-</WRAP> 
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- * **August 29th, Wednesday ** (3:30-4:30pm)\\  \\   **//Speaker //**:  \\      **//Topic//**: organizational meeting  \\     \\  + * **August 29th, Wednesday ** (3:30-4:30pm)\\   
 +\\   **//Speaker //**:   
 +\\      **//Topic//**: organizational meeting  \\     \\  
 \\ \\  \\ \\ 
  
- * **September 5th, Wednesday ** (3:30-5:00pm)(No talk due Monday schedule)\\  \\   **//Speaker //**:   \\      **//Topic//**:   No talk + * **September 5th, Wednesday ** (3:30-5:00pm)(No talk due Monday schedule)\\   
 +\\   **//Speaker //**:    
 +\\      **//Topic//**:   No talk 
 \\ \\   \\ \\  
 <WRAP box 80%> **//Abstract//**:    <WRAP box 80%> **//Abstract//**:   
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- * **September 12th, Wednesday ** (3:30-4:55pm)\\  \\   **//Speaker //**:  Gang Zhou (Binghamton University) \\      **//Topic//**: A description of generic singularities formed by mean curvature flow+ * **September 12th, Wednesday ** (3:30-4:55pm)\\   
 +\\   **//Speaker //**:  Gang Zhou (Binghamton University)  
 +\\      **//Topic//**: A description of generic singularities formed by mean curvature flow
 \\ \\   \\ \\  
 <WRAP box 80%> **//Abstract//**: In this talk I will present the progresses my collaborators, including Michael Sigal and Dan Knopf, and I made in the past few years. We developed a new way of studying mean curvature flow, and I am trying to use it to understand the evolution of hypersurfaces under mean curvature flow. <WRAP box 80%> **//Abstract//**: In this talk I will present the progresses my collaborators, including Michael Sigal and Dan Knopf, and I made in the past few years. We developed a new way of studying mean curvature flow, and I am trying to use it to understand the evolution of hypersurfaces under mean curvature flow.
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- * **September 19th, Wednesday ** (3:30-4:55pm)(Holiday, Yom Kippur)\\  \\  **// Speaker //**:  \\      **//Topic//**:   + * **September 19th, Wednesday ** (3:30-4:55pm)(Holiday, Yom Kippur)\\  
 + \\  **// Speaker //**:   
 +\\      **//Topic//**:   
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 <WRAP box 80%> **//Abstract//**:  <WRAP box 80%> **//Abstract//**: 
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-* **September 26th , Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**: Adam Weisblatt (Binghamton University)  \\      **//Topic//**: The heat equation on planar diagrams.   +* **September 26th , Wednesday ** (3:30-4:55pm) \\   
 +\\   **//Speaker//**: Adam Weisblatt (Binghamton University)   
 +\\      **//Topic//**: The heat equation on planar diagrams.   
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:  The heat kernel on a surface helps to describe its geometry. <WRAP box 80%> **//Abstract//**:  The heat kernel on a surface helps to describe its geometry.
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- * **October 3rd, Wednesday ** (3:30-4:55pm)\\  \\   **//Speaker//**: Brian Allen (West Point) \\ \\     **//Topic//**: Stability Questions and Convergence of Riemannian Manifolds  + * **October 3rd, Wednesday ** (3:30-4:55pm)\\   
 +\\   **//Speaker//**: Brian Allen (West Point) \\  
 +\\     **//Topic//**: Stability Questions and Convergence of Riemannian Manifolds  
 \\     \\ \\     \\
 <WRAP box 80%> **//Abstract//**: We will start by surveying the stability of the scalar torus rigidity theorem, a result about the impact of geometry on topology, and the stability of the positive mass theorem, an important theorem in mathematical relativity. Since stability requires a notion of closeness this will lead us naturally to consider various notions of distance between and  convergence of Riemannian manifolds. We will end by discussing theorems and important examples which aim at contrasting these notions of convergence which have been, and will continue to be, applied to stability problems. <WRAP box 80%> **//Abstract//**: We will start by surveying the stability of the scalar torus rigidity theorem, a result about the impact of geometry on topology, and the stability of the positive mass theorem, an important theorem in mathematical relativity. Since stability requires a notion of closeness this will lead us naturally to consider various notions of distance between and  convergence of Riemannian manifolds. We will end by discussing theorems and important examples which aim at contrasting these notions of convergence which have been, and will continue to be, applied to stability problems.
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-  
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-* **October 10th, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**:  \\      **//Topic//**:    
-\\     \\   
-<WRAP box 80%> **//Abstract//**:  
- 
- \\ 
-</WRAP> 
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- * **October 17th, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**: Shengwen Wang (Binghamton University) \\      **//Topic//**: Mean curvature flow with surgery and applications  + * **October 17th, Wednesday ** (3:30-4:55pm) \\   
 +\\   **//Speaker//**: Shengwen Wang (Binghamton University)  
 +\\      **//Topic//**: Mean curvature flow with surgery and applications  
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**: I will first review about mean curvature flow with surgery for 2-convex hypersurfaces. Then I will report on joint work with Mramor for mean curvature flow with surgery for low entropy mean-convex hypersurfaces and an application to the classification of self-shrinkers. I will also discuss what elements we still lack to do surgery for generic mean curvature flow.   <WRAP box 80%> **//Abstract//**: I will first review about mean curvature flow with surgery for 2-convex hypersurfaces. Then I will report on joint work with Mramor for mean curvature flow with surgery for low entropy mean-convex hypersurfaces and an application to the classification of self-shrinkers. I will also discuss what elements we still lack to do surgery for generic mean curvature flow.  
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-* **October 24th, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**:  Lu Zhang (Binghamton University)  \\      **//Topic//**: Some useful methods for Fourier multipliers   +* **October 24th, Wednesday ** (3:30-4:55pm) \\   
 +\\   **//Speaker//**:  Lu Zhang (Binghamton University)   
 +\\      **//Topic//**: Some useful methods for Fourier multipliers   
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:  I will give a introduction of some methods that have been recently used to study the Lp bounds for the multi-parameter Fourier multipliers, which include one method that was applied in my recent work.   <WRAP box 80%> **//Abstract//**:  I will give a introduction of some methods that have been recently used to study the Lp bounds for the multi-parameter Fourier multipliers, which include one method that was applied in my recent work.  
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- * **October 31st, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**: Xiangjin Xu (Binghamton University )  \\      **//Topic//**:  New heat kernel estimates on manifolds with negative Ricci curvature+ * **October 31st, Wednesday ** (3:30-4:55pm) \\   
 +\\   **//Speaker//**: Xiangjin Xu (Binghamton University )   
 +\\      **//Topic//**:  New heat kernel estimates on manifolds with negative Ricci curvature
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**: In this talk, we first introduce some new sharp Li–Yau type gradient estimates, <WRAP box 80%> **//Abstract//**: In this talk, we first introduce some new sharp Li–Yau type gradient estimates,
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- + * **November 14th, Wednesday ** (3:30-4:55pm)  \\   
-* **November 7th, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**: \\      **//Topic//**:     +\\   **//Speaker//**:  Phil Sosoe, Cornell University 
-\\     \\   +\\      **//Topic//**:  Applications of CLTs and homogenization for Dyson Brownian Motion 
-<WRAP box 80%> **//Abstract//**:    +
- +
-</WRAP> +
-\\ \\  +
- +
- +
- +
- * **November 14th, Wednesday ** (3:30-4:55pm)  \\  \\   **//Speaker//**:  Phil Sosoe, Cornell University\\      **//Topic//**:  Applications of CLTs and homogenization for Dyson Brownian Motion +
 to Random Matrix Theory to Random Matrix Theory
 \\     \\   \\     \\  
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-* **November 21st, Wednesday ** (3:30-4:55pm)(Thanksgiving break)\\  \\   **//Speaker//**:    \\      **//Topic//**:  +* **November 21st, Wednesday ** (3:30-4:55pm)(Thanksgiving break)\\   
 +\\   **//Speaker//**:     
 +\\      **//Topic//**:  
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:  <WRAP box 80%> **//Abstract//**: 
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- * **November 28th, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**: Martin Fraas, Virginia Tech  \\      **//Topic//**:   Perturbation Theory of Quantum Trajectories+ * **November 28th, Wednesday ** (3:30-4:55pm) \\   
 +\\   **//Speaker//**: Martin Fraas, Virginia Tech   
 +\\      **//Topic//**:   Perturbation Theory of Quantum Trajectories
 \\     \\   \\     \\  
 <WRAP box 80%> **//Abstract//**:  Quantum trajectories are certain Markov processes on a complex projective space. They describe the evolution of a quantum system subject to a repeated indirect measurement. For a given set of matrices $A$ and a unit vector $x$, a probability of a sequence of matrices $V_1, V_2, \dots , V_n$, $Vj \in A$ is proportional to $||V_n \dots V_1x||^2$. The Markov process is given by $x_n \sim V_n \dots V_1 x$. In this talk, I will review the basic properties of this process, in particular, conditions that guarantee the uniqueness of the stationary measure. Then I will discuss how the measure and the process change if the underlying set of matrices A changes. <WRAP box 80%> **//Abstract//**:  Quantum trajectories are certain Markov processes on a complex projective space. They describe the evolution of a quantum system subject to a repeated indirect measurement. For a given set of matrices $A$ and a unit vector $x$, a probability of a sequence of matrices $V_1, V_2, \dots , V_n$, $Vj \in A$ is proportional to $||V_n \dots V_1x||^2$. The Markov process is given by $x_n \sim V_n \dots V_1 x$. In this talk, I will review the basic properties of this process, in particular, conditions that guarantee the uniqueness of the stationary measure. Then I will discuss how the measure and the process change if the underlying set of matrices A changes.
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-* **December 5th, Wednesday ** (3:30-4:55pm) \\  \\   **//Speaker//**: Kunal Sharma (Binghamton University)    \\      **//Topic//**:   +* **December 5th, Wednesday ** (3:30-4:55pm) \\   
 +\\   **//Speaker//**: Kunal Sharma (Binghamton University)     
 +\\      **//Topic//**:   
  
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seminars/anal/2014_2015.1751338149.txt · Last modified: (external edit)