The area starts with Galois and Gauss.  Group theory and exponential sums were the two application areas then.  That tradition continues.

• Without Chevalley groups over  finite  fields there would have been no structure theory of  finite simple groups.
  
• Weil's Riemann Hypothesis for curves over  finite  fields is a singular event – Many error estimates in combinatorics derive from  it.
  

Research in  finite  fields requires combinatorial understanding of many examples. This is true in myriad applications  coding theory  exceptional polynomials  and covers,   algorithmic applications of elimination of quantiers, diophantine relations between curves over number fields and their reductions modulo p,
 probabilistic algorithms over  finite  fields.  Yet, there are powerful general abstract tools  Consider two premiere mathematical events from the last twenty  five years.

• Deligne's proof of the general Weil conjectures.
• The classification of  finite simple groups. 
  

This conference's papers offer examples of applying such tools to practical researcher specialties.  The sections of this preface divide along the basic
themes of the conference.  The preface makes several connections not appearing directly in the papers  Some papers in the conference refer directly to Bernie
Dwork (who died not long after attending the conference),  not only to his papers.   This preface's sections includes comments giving an overview of his work.  It compliments the article    N. Katz and J. Tate,  B. Dwork 1923–1998, Notices of the AMS   46  3, 338–343.     

§1. Beyond Weil bounds  curves with many rational points

• Ihara: The moduli space approach
• Xing: The Drinfeld module approach when q is not a square
• Hayes: More on explicit use of Drinfeld modules
• Van der Geer: One curve with many points and  fiber products
• Garcia: Approach from classical curves
  

§2. Monodromy groups of characteristic p covers

• Guralnick: What to expect of monodromy groups from genus 0  covers
• Abhyankar: Abhyankar's approach
• Elkies: Reflection on classical invariant theory
• Deschamps: Reduction mod p and  field of moduli of covers
• Dèbes: Refined abelian covers
• Emsalem: Good reduction of covers
• Huang: Explicit computation of monodromy groups over  finite  fields
  

§3. Zeta functions and trace formulas

• Wan: Unit root L functions
• Sperber: Zeta functions of complete intersections
• Leprévost: Properties of a modular curve quotient
• Li: Appearance of rank  1 representations in L functions for higher dimensional representations
• Chung: Eigenvalues of a Laplacian
• Rosen: Average values of Zeta functions and elliptic surfaces
  

§4. A short dedication to the work of Bernard Dwork 

• Michael Rosen:  Dwork's relation to his students  
  
• Pierre Dèbes:  Dwork's role in G Functions
• Alan Adolphson: Dwork's  Final conjecture