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seminars:anal [2026/03/12 16:45] – xxuseminars:anal [2026/08/06 18:26] (current) – xqiao
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 =====The Analysis Seminar===== =====The Analysis Seminar=====
  
-[[http://www-history.mcs.st-and.ac.uk/Mathematicians/Fourier.html|Fourier]]+[[https://www-history.mcs.st-and.ac.uk/Mathematicians/Fourier.html|Fourier]]
  
 The seminar meets Wednesdays in WH-100E at 4:00-5:00 p.m. There are refreshments and snacks in WH-102 at 3:15. The seminar meets Wednesdays in WH-100E at 4:00-5:00 p.m. There are refreshments and snacks in WH-102 at 3:15.
  
 **Organizers**:\\  **Organizers**:\\ 
-**Faculy:**[[:people:loya:start|Paul Loya]], [[:people:renfrew:start|David Renfrew]], [[:people:mrostami:start|Minghao Rostami]], [[:people:ewyman:start|Emmett Wyman]], [[:people:xxu:start|Xiangjin Xu]], [[:people:zxu24:start|Ziyao Xu]] and [[:people:gzhou:start|Gang Zhou]]\\ +**Faculty: **[[:people:loya:start|Paul Loya]], [[:people:renfrew:start|David Renfrew]], [[:people:mrostami:start|Minghao Rostami]], [[:people:ewyman:start|Emmett Wyman]], [[:people:xxu:start|Xiangjin Xu]], [[:people:zxu24:start|Ziyao Xu]] and [[:people:gzhou:start|Gang Zhou]]\\ 
-**Post-Docs:**  [[:people:rsarkar2:start|Rohan Sarkar]]+**Post-Docs:**  [[:people: :start| ]]
  
 [[http://www.math.binghamton.edu/dept/AnalysisSem/index.html|Previous talks]] [[http://www.math.binghamton.edu/dept/AnalysisSem/index.html|Previous talks]]
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 +====Fall 2026====
  
 + 
 +* **August 19th, Wednesday ** (4:00-5:00pm)\\  \\   
 +**//Speaker //**:  \\      
 +**//Topic//**: organizational meeting  \\     \\  
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 + * **September 23rd, Wednesday ** (4:00-5:00pm) \\  \\  
 +**// Speaker //**:   \\      
 +**//Topic//**:   
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 + * **October 7th, Wednesday ** (4:00-5:00pm)\\  \\   
 +**//Speaker//**:    \\ \\     
 +**//Topic//**:  
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 +<WRAP box 80%> 
 +**//Abstract//**:  
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 +</WRAP>     
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 +
 +* **November 25th, Wednesday ** (4:00-5:00pm) (Thanksgiving Break)\\  \\   
 +**//Speaker//**:  Thanksgiving Break  \\      
 +**//Topic//**:  
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 +
 +* **December 2nd, Wednesday ** (4:00-5:00pm)\\  \\   
 +**//Speaker//**:  \\      
 +**//Topic//**:  
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 +<WRAP box 80%> **//Abstract//**: 
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- * **March 18th, Wednesday ** (4-5pm) \\  \\  + * **(Updated) March 19th, Thursday ** (4-5pm) \\  \\  
  **//Speaker//**: Zheng Sun (University of Alabama, Tuscaloosa)\\       **//Speaker//**: Zheng Sun (University of Alabama, Tuscaloosa)\\     
  **//Topic//**: On a numerical artifact of solving shallow water equations with a discontinuous bottom  **//Topic//**: On a numerical artifact of solving shallow water equations with a discontinuous bottom
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 * **March 25th, Wednesday ** (4-5pm) \\  \\    * **March 25th, Wednesday ** (4-5pm) \\  \\   
 **//Speaker//**:   Yiming Zhao(Syracuse University) \\       **//Speaker//**:   Yiming Zhao(Syracuse University) \\      
-**//Topic//**:  TBD+**//Topic//**:  $SL(n)$-invariant isoperimetric and Minkowski problems
 \\     \\   \\     \\  
-<WRAP box 80%> **//Abstract//**: +<WRAP box 80%> **//Abstract//**: In convex geometry, where convex bodies are the primary objects of study, a central goal is to discover geometric invariants and measures that can be used to recover or characterize their shapes. Two intertwined lines of research pursue this objective. Isoperimetric inequalities involving geometric invariants, including the classical isoperimetric inequality and the celebrated Brunn–Minkowski inequality, seek to identify special shapes as extremals. Minkowski problems, a family of problems originating in the work of Minkowski, aim to recover, sometimes uniquely, the shape of an arbitrary convex body by solving measure equations that, under additional but unnecessary smoothness assumptions, reduce to Monge–Ampère-type equations. In this talk, after giving some historical background, I will discuss recent joint work with Dongmeng Xi that continues this line of research through the study of integral affine surface area and radial mean bodies.
  
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 * **April 1st, Wednesday ** (4-5pm) \\  \\   * **April 1st, Wednesday ** (4-5pm) \\  \\  
- **//Speaker//**:  Spring Break  \\       + **//Speaker//**:  Spring Break (Binghamton University) \\       
-**//Topic//**:    +**//Topic//**:  A lower bound on sleep duration under optimal conditions  
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 <WRAP box 80%> **//Abstract//**:    <WRAP box 80%> **//Abstract//**:   
  
 +We show that in the absence of homework, sleep duration increases without bound. Applications to stress reduction are discussed.
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  * **April 8th, Wednesday ** (4-5pm)  \\  \\    * **April 8th, Wednesday ** (4-5pm)  \\  \\  
- **//Speaker//**:   \\      + **//Speaker//**:  Gang Zhou (Binghamton University) \\      
- **//Topic//**:   + **//Topic//**:   Exact characterizations for quantum conditional mutual information and some other entropies
 \\     \\   \\     \\  
-<WRAP box 80%> **//Abstract//**:   +<WRAP box 80%> **//Abstract//**:   I will present my latest results on quantum information theory. I will start with an introduction to the quantum theory for preparation, and then present the results. 
 + 
 +Lieb and Ruskai's strong subadditivity theorem, which shows that the conditional mutual information must be nonnegative, is fundamental in quantum theory. It has numerous applications, such as in quantum error correction.  
 + 
 +When the mutual information is zero, the Petz recovery map can be used to reconstruct the quantum channel.  
 + 
 +When the mutual information is small, one seeks to define an optimal recovery channel. To this end, a mathematical characterization of the mutual information is desirable. In my latest paper I provided an exact characterization of the mutual information, along with characterizations for other entropies. My controls are sharp, leaving no room for improvement, in the sense that I provided equalities, regardless of whether the mutual information (or remainder) is small or large. 
 + 
 +I transformed the definitions of these entropies into a summation of explicitly constructed terms, and the definition of each term obviously demonstrates the desired positivity/convexity/concavity. The summation converges rapidly and absolutely in a chosen elementary norm.
  
 +An exposition for the general public was provided by git.science and emailed to me, see the link https://gist.science/paper/2603.14650
      
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 * **May 6th, Wednesday ** (4-5pm) \\  \\   * **May 6th, Wednesday ** (4-5pm) \\  \\  
- **//Speaker//**: \\      + **//Speaker//**:Santiago Alzate (Binghamton University) \\      
- **//Topic//**: + **//Topic//**: Masters thesis
  
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seminars/anal.1773333946.txt · Last modified: by xxu