Intersections of Schubert Varieties<br>
Corey Irving<br>
Texas A&M University<br>
Milner 313<br>
4:00-5:00<br>
24 JAN 2008<br>
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Schubert varieties are subvarieties of the Grassmannian.  Many interesting geometric problems can be interpreted in 
terms of intersections of these varieties.  The intersection can be studied by associating to a Schubert variety an 
element of a ring where the multiplication can be viewed as intersection.  The multiplication in the ring may easily 
be performed by a simple combinatorial formula due to Pieri. <br> 
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In this talk I will discuss the zero-dimensional intersection of Schubert varieties. The classical Schubert problem of four 
lines, which asks how many lines in space meet four fixed lines, will be examined.  I'll show how to model this problem as 
an intersection of Schubert varities, then use Pieri's formula to calculate the answer.  This theory requires working over 
an algebraically closed field.  If the Shubert problem is posed in real terms, the results above may include complex points 
of intersection.  Lastly, I'll describe some special cases where the intersection points are all real, which includes some 
current work. <br>