#  Seminar: Frederick Manners (University of California, San Diego): "Inverse theorems and approximate structure" 

 



####  calendar\_today Date and Time 

 **January 30, 2024** 

 04:30PM - 05:30PM EST 

####  pin\_drop Location 

 **Jefferson 256 and Zoom**  



 

 



 

   ![Frederick Manners](/sites/g/files/omnuum6611/files/styles/hwp_1_1__360x360_scale/public/mathpicture/files/frederick_manners.jpg?itok=-3yxsmZD) 

 

  
Zoom link: <https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09>  
Speaker: Frederick Manners (University of California, San Diego)  
Title: **Inverse theorems and approximate structure**  
Abstract: We call a function f linear if f(x+y) = f(x) + f(y) holds for all x,y. It is natural to call f "99% linear" if instead this identity holds for most pairs (x,y); say, 99% of pairs. Similarly, we could say f is "1% linear" if this identity holds 1% of the time. A natural question is then: what can we say about the structure of "99% linear" or "1% linear" functions? Are they always just perturbations of true 100% linear functions, or are there other examples?  
   
Given almost any algebraic definition, you can similarly ask about its approximate variants, and if you can prove a strong positive statement, it tends to have applications. In particular, I will discuss how 1% linear functions relate to the Polynomial Freiman-Ruzsa conjecture, and how 1% polynomial functions relate to the Inverse Theorem for the Gowers norms.

 

 



 

 

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