Title: Zeros of quadratic forms over function fields of p-adic
curves </br> </br> Abstract: </br>

</br> It was an open question until late 90's whether quadratic
forms in sufficiently large number of variables over function
fields  of p-adic curve represent zero nontrivially; conjecturally
every quadratic form in at least nine variables represents zero
nontrivially. This is still wide open. We explain results
concerning this question and show how they could be used to
construct examples of projective homogeneous spaces under simply
connected groups over such fields with no rational points which
admit  zero cycles of degree one.